(navigation image)
Home American Libraries | Canadian Libraries | Universal Library | Community Texts | Project Gutenberg | Children's Library | Biodiversity Heritage Library | Additional Collections
Search: Advanced Search
Anonymous User (login or join us)
Upload
See other formats

Full text of "Physics"

/ 




Qtfyt library 

of tlje 
Babtb Bunlap tf^bgerbatorp 



presented op 

C... A... Chant 

January 19 57 



I& 



% -io 



PHYSICS 

TOWER, SMITH, TURTON, 

AND 

COPE 




(See p.441) 

Three-color Printing 
Y. Yellow impression; negative made through a blue-violet filter. R. Crimson 
impression; negative made through a green filter. RY. Crimson on yellow. 
B. Blue impression; negative made through a red filter. YRB. Yellow, crim- 
son, and blue combined; the final product. (Courtesy of Phototype Engraving 
Co., Philadelphia.) 



PHYSICS 



BY 

WILLIS E. TOWER, M. SCI. (Univ. of Illinois) 

HEAD OF THE DEPARTMENT OF PHYSICS, ENGLEWOOD 
HIGH SCHOOL, CHICAGO 

CHARLES H. SMITH, M. E. (Cornell) 

HEAD OF THE DEPARTMENT OF PHYSICS AND ASSISTANT 
PRINCIPAL, HYDE PARK HIGH SCHOOL, CHICAGO 

CHARLES M. TURTON, A. M. (Syracuse) 

HEAD OF THE DEPARTMENT OF PHYSICS, BOWEN 
HIGH SCHOOL, CHICAGO 

IN COLLABORATION WITH 

THOMAS D. COPE, PH.D. (Pennsylvania) 

ASSISTANT PROFESSOR OF PHYSICS, UNIVERSITY 
OF PENNSYLVANIA 



BASED UPON 

PRINCIPLES OF PHYSICS 

BY 
TOWER, SMITH and TURTON 



WITH 7 PLATES AND 448 OTHER ILLUSTRATIONS 



PHILADELPHIA 

P. BLAKISTON'S SON & CO. 

1012 WALNUT STREET 



** 



rfe 



Copyright, 1920, by P. Blakiston's Son & Co. 



)-7 




THE MAP 



PREFACE 



In the preparation of this text, the pupil, his experience, 
needs, and interests have been constantly kept in mind. 
The order of topics, illustrations, and problems have 
been selected with the purpose of leading the pupil into 
a clear understanding of the physical phenomena continu- 
ally taking place about him. 

The recommendations and conclusions reached by the 
"New Movement in the Teaching of Physics" have been 
incorporated into the book as a whole. These conclusions 
indicate that the most efficient teaching in physics involves 
a departure from the quantitative, mathematical methods 
of presentation that were in general use a dozen or more 
years ago, toward a method better adapted to the capa- 
bilities, interests, and requirements of the young people in 
our physics classes. 

The older methods are effective with a portion of the 
student body which has the greater mathematical ability 
and training, but they discourage a large majority of the 
pupils who are not gifted or prepared for severe mathe- 
matical analysis. For this reason, many of the more dif- 
ficult mathematical demonstrations often given in physics 
texts are omitted. Most of the problems involve only the 
units employed in practical every-day measurements. 

The portions of Mechanics that are ordinarily so diffi- 
cult for the average pupil are not taken up until he has 
covered considerable ground with which he is more or less 
familiar and not until he has become somewhat accustomed 



VI PREFACE 

to the methods of study and the technical terms of the 
subject. 

The pupil comes to the study of physics with a great 
number of experiences and impressions of physical phe- 
nomena continually occurring about him. In recognition 
of this fact, it has been thought best to consider first the 
explanation of common things well known to all pupils, 
such as the diffusion of gases, evaporation of liquids, 
expansion of bodies when heated, and capillary action. 
Since the molecular theory of matter is now supported by 
so many conclusive evidences, we have not hesitated to 
make free use of it in the early chapters. The applications 
of this theory are extremely helpful in explaining every-day 
phenomena. Our experience shows that beginners in phys- 
ics understand and apply this theory without difficulty. 

The illustrations .and drawings have been selected from 
a pedagogical rather than a spectacular point of view. 
Practically all of them are new. The problems and exer- 
cises have been selected for the distinct purpose of illus- 
trating the principles taught in the text and for their 
practical applications. 

Many direct applications to common every-day experi- 
ences are given in order to connect the subject matter with 
the home environment and daily observation of physical 
phenomena. Some phenomena are mentioned without 
detailed explanation as it is felt that the presentation of 
these subjects in this manner is better for this grade of 
student than a complete analysis. 

Some of the special features of the text may be briefly 
summarized as follows: 

(A) Simplicity of presentation is emphasized. The 
methods of attack, the illustrations' and examples em- 
ployed in developing the subjects are particularly adapted 
to beginners in physics. 



PREFACE Vll 

(B) The text is divided into some seventy-seven sections, 
each containing material enough for one recitation. 

(C) Each of these sections is summarized by a list of 
important topics which point out to the pupil the princi- 
ples and subject matter requiring most careful attention. 
The lists of important topics are also of assistance to the 
teacher in assigning recitations. 

(D) The problems and practical exercises emphasize 
physical principles as distinguished from mathematical 
training. A list of exercises is placed at the end of the 
several sections. They are in sufficient number to permit 
testing at many points and of a choice of problems by 
teachers. 

The authors wish to express their appreciation for sug- 
gestions and helpful criticisms to many who have read the 
text in manuscript or proof. Especially to Professor A. P. 
Carman of the University of Illinois and his associate, 
Professor F. R. Watson, who have gone carefully over the 
whole text; and to Mr. Chas. M. Brunson, Scott High 
School, Toledo, Ohio, Mr. Frank E. Goodell, North High 
School, Des Moines, Iowa, and to Mr. Walter R. Ahrens, 
Englewood High School, Chicago, for assistance in read- 
ing the proofs. Also to Mr: W. H. Collins, Jr., Bowen 
High School, Chicago, who supervised the preparation of 
drawings for the diagrams and figures; and to many firms 
and individuals that have courteously furnished material 
for illustrations. 

Willis E. Tower. 

Charles H. Smith. 

Charles M. Turton. 



ON THE STUDY OF PHYSICS 



When a pupil begins the study of Physics he has in his 
possession many bits of knowledge which are fundamental 
in the science. He has learned to throw a ball and can tell 
how a thrown ball moves. He has drawn out nails with a 
claw hammer. He has seen wood float and iron sink. He 
has sucked liquids up through straws. In his mother's 
kitchen, he sees water as ice, liquid, and steam. On a 
wintry day he reads the temperature on a thermometer. 
He sees sparks fly from car wheels when the brakes are 
applied. He has played with a horseshoe magnet, and has 
found the north by means of a compass. The telephone, 
the electric light and the motor he s'ees, and perhaps uses, 
many times a day. He dresses before a mirror, focuses 
his camera, watches the images at a moving picture 
show, and admires the colors of the rainbow. He has 
cast stones into water to watch the ripples spread, has 
shouted to hear the echo, and perhaps plays some musical 
instrument. These, and a thousand other things, are 
known to the intelligent and normal boy or girl who has 
reached the age at which the study of Physics is properly 
begun. 

To a great extent even the terms used in the science are 
familiar to the beginner. He speaks of the horsepower 
of an engine, reads kilowatt-hours from the meter in the 
cellar, and may know that illuminating gas costs one 
dollar per thousand ' ' cubic f eet. " " Ampere ' ' and ' - volt ' ' 
are words he frequently hears and sees. 

When he takes up the study of Physics, the attitude of 



X ON THE STUDY OF PHYSICS 

the student toward these familiar things and words must 
undergo a change. Casual information about them must 
be changed to sound knowledge, purposely acquired. 
Hazy notions about the meanings of words must be 
replaced by exact definitions. Bits of knowledge must 
be built into a structure in which each fact finds its proper 
place in relation to the others. 

The only agent which can accomplish these changes is 
the student himself. He must consciously and pur- 
posely seek the truth and must reflect upon it until he 
sees it in its relation to other truth. Upon him, and upon 
him alone, rests the final responsibility for the success or 
failure of his study. 

But the student is not without assistance. In his 
teacher he finds a guide to stimulate, to direct, and to aid 
his efforts, and a critic to point out wherein his efforts 
have failed and wherein they have succeeded. Weights, 
measures, and other apparatus are furnished to enable 
him to answer for himself questions which have arisen in 
his studies. 

In addition to these the student has his text book, his 
teacher for his hours of private study. A good text book 
is an inspiring teacher in print. It directs attention to 
things familiar to the student through long experience, and 
inspires him to make a closer scrutiny of them. It invites 
him to observe, to analyze, to compare, to discover like- 
nesses and differences in behavior. It questions him at 
every turn. Its ever repeated challenge reads, "Weigh 
and consider." It furnishes him needed information that 
he cannot otherwise acquire. It satisfies his desire to 
know, "By whom, where, when, and how was this first 
discovered?" 

The student of Physics must never forget that he is 
studying not pages of text but the behavior and properties 



ON THE STUDY OF PHYSICS XI 

of iron, water, mica, moving balls, pumps, boiling liquids, 
compressed air, mirrors, steam engines, magnets, dynamos, 
violins, flutes, and a host of other things. His studies 
should, whenever possible, be made first hand upon the 
things themselves. The text is an aid to study, never a 
substitute for the thing studied. 

It is an excellent plan for each student to select some 
one thing for special study, the telephone for example. 
By observation, experiment, and reading, he may acquire 
a large amount of valuable information about such a 
subject while pursuing his course in Physics. Every part 
of the science will be found to bear some relation to it. 

The student who takes up the study of Physics in the 
way suggested will find himself at the end of a year of 
study in possession of much new and valuable knowledge 
about the physical world in which he lives. By virtue 
of this knowledge he will be better able to enjoy the world, 
to control it, and to use it. 

Thomas D. Cope. 

Philadelphia. 



CONTENTS 



Chapter I. Introduction and Measurement. Page 

(ij) Introduction I 

(2) States of Matter 4 

(3) The Metric System , 8 

Chapter II. Molecular Forces and Motions. 

(1) Molecular Motions in Gases 13 

(2) Molecular Motions in Liquids 18 

(3) Molecular Forces in Liquids 21 

(4) Molecular Fortes in Liquids and Solids . . 27 

(5) Molecular Forces in Solids 31 

Chapter III. Mechanics of Liquids. 

(1) Liquid Pressure 36 

(2) Transmission of Liquid Pressure 41 

(3) Archimedes' Principle 47 

(4) Density and Specific Gravity 52 

Chapter IV. Mechanics of Gases. 

(1) Weight and Pressure of the Air 55 

(2) Compressibility and Expansibility of the Air 62 

(3) Pneumatic Appliances 66 

Chapter V. Force and Motion. 

(1) Force, how Measured and Represented 79 

(2) Motion. Newton's Laws 85 

(3) Resolution of Forces 96 

(4) Moment of Force and Parallel Forces 99 

(5) Gravitation and Gravity 103 

(6) Falling Bodies 109 

(7) The Pendulum 115 

Chapter VI. Work and Energy. 

(1) Work and Energy 119 

(2) Power and Energy 123 

(3) The Lever and Simple Machines 129 

(4) Wheel and Axle and Pulley 136 

(5) Efficiency and the Inclined Plane 142 

(6) Friction and its Uses 147 

(7) Water Power 152 

xiii 



XIV CONTENTS 

Chapter VII. Heat, Its Production and Transmission. page 

(i) Sources and Effects of Heat 159 

(2) Temperature and Expansion 162 

(3) Expansion of Gases, Liquids and Sclids 167 

(4) Modes of Transmitting Heat 173 

(5) Convection, Heating and Ventilation 179 

(6) The Moisture in the Air, Hygrometry 191 

(7) Evaporation 196 

Chapter VIII. Heat and Work. 

(1) Heat Measurement and Specific Heat 200 

(2) Heat and Changes of State 205 

(3) Heat and Work 212 

(4) Heat Engines 222 



Chapter IX. Magnetism. 

(1) General Properties of Magnets 228 

Theory of Magnetism, Magnetic Fields 232 

The Earth's Magnetism 238 



a 



Chapter X. Static Electricity. 

(1) Electrification and Electrical Charges 243 

(2) Electric Fields and Electrostatic Induction 247 

(3) Electric Theories, Distribution and Electric Charges. . 252 

(4) Potential, Capacity, and the Electric Condenser . . .257 

(5) Electrostatic Generators 262 



Chapter XL Electric Currents Produced by Voltaic 
Cells. 

(1) Electrical Currents and Circuits. 267 

The Simple Voltaic Cell and its Action 270 

Practical Voltaic Cells 274 



8 



Chapter XII. Magnetic Effects of Electric Currents, 
and Electrical .Measurements. 

The Magnetic Effect of Electric Currents 279 

Electrical Measurements 289 

(3) Ohm's Law and Electrical Circuits 298 

(4) Grouping of Cells and Measuring Resistance 302 



(2 



Chapter XIII. Chemical and Heat Effects of Electric 

Currents. 

(1} The Chemical Effect of Electric Currents 307 

(2) The Storage Battery and Electric Power 312 

(3) The Heat Effect of Electric Currents 318 

Chapter XIV. Induced Currents. 

(1) Electromagnetic Induction 326 

(2) The Dynamo and the Motor 335 

(3) The Induction Coil and the Transformer 343 

(4) The Telephone 349 



CONTENTS XV 

Chapter XV. Sound. Page 

(i) Sound, Source, Speed, Media 354 

(2) Waves and Wave Motion 357 

(3) Intensity and Pitch of Sound 363 

(4) Musical Scales and Resonance 368 

(5) Interference, Beats, Vibration of Strings 374 

(6) Tone Quality, Vibrating Plates and Air Columns . . . 384 



Chapter XVI. Light. 

(1) Rectilinear Propagation of Light 388 

(2) Photometry and Law of Reflection 393 

(3) Mirrors and Formation of Images 400 

(4)' Refraction of Light 410 

(5) The Formation of Images by Lenses. 416 

(6) Optical Instruments 423 

(7) Color and Spectra 430 

(8) Nature of Light ' 442 



Chapter XVII. Invisible Radiations. 

(1) Electric Waves and Radioactivity 448 

Chapter XVIII. Wireless Telephony and Alternating 
Currents. 

(1) Wireless Telephony 460 

(2) Alternating Currents 466 

Index 487 



PHYSICS 

CHAPTER I 
INTRODUCTION AND MEASUREMENT 

(i) Introduction 

i. Physics, an Explanation of Common Things. Many 
students take up the study of physics expecting to see 
wonderful experiments with the "X" rays, wireless teleg- 
raphy, dynamos, and other interesting devices. Others 
are dreading to begin a study that to them seems strange 
and difficult, because they fear it deals with ideas and 
principles that are beyond their experience and hard to 
comprehend. 

Each of these classes is surprised to learn that physics 
is mainly an explanation of common things. It is a study 
that systematizes our knowledge of the forces and changes 
about us; such as the pull of the earth, the formation of 
dew, rain and frost, water pressure and pumps, echoes 
and music, thermometers and engines, and many other 
things about us with which people are more or less familiar. 
Physics is like other school subjects, such as mathematics 
and language, in having its own peculiar vocabulary and 
methods of study; these will be acquired as progress is 
made in the course. 

The most useful habit that the student of physics can 

I 



2. PHYSICS 

form is that of connecting or relating each new idea or 
fact that is presented to him to some observation or expe- 
rience that will illustrate the new idea. This relating 
or connecting of the new ideas to one's own personal 
experience is not only one of the best known means of 
cultivating the memory and power of association, but it 
is of especial help in a subject such as physics, which deals 
with the systematic study and explanation of the facts 
of our every-day experience. 

2. Knowledge Common and Scientific. This leads 
to the distinction between common knowledge and scientific 
knowledge. We all possess common knowledge of the 
things about us, gained from the impressions received by 
our senses, from reading, and from the remarks of others. 
Scientific knowledge is attained when the bits of common 
knowledge are connected and explained by other informa- 
tion gained through study or experience. That is, com- 
mon knowledge becomes scientific, when it is organized. 
This leads to the definition : Science is organized knowledge. 

Common knowledge of the forces and objects about 
us becomes scientific only as we are able to make accurate 
measurements of these. That is, science is concerned 
not only in how things work, but even more in how much 
is involved or results from a given activity. For example, 
a scientific farmer must be able to compute his costs and 
results in order to determine accurately his net profits. 
The business man who is conducting his business with 
efficiency knows accurately his costs of production and 
distribution. 

This book is written in the hope that it will make more 
scientific the student's common knowledge of the forces 
and changes in the world about him and will give him many 
ideas and principles that will help him to acquire the 
habit of looking from effects to their natural causes and 



INTRODUCTION AND MEASUREMENT 3 

thus tend to develop what is called the scientific habit of 
thought. 

3. Hypothesis, Theory, and Law. Three words that 
are frequently used in science may be mentioned here: 
hypothesis, theory, and law. An hypothesis is a supposition 
advanced to explain some effect, change, or condition that 
has been observed. For example, the Nebular Hypothe- 
sis of which many high-school students have heard, is an 
attempt to explain the origin of the sun, the earth, the 
planets, and other solar systems. 

A theory is an hypothesis which has been tested in a 
variety of ways and which seems to fit the conditions and 
results so that it is generally accepted as giving a satis- 
factory explanation of the matter in question. The 
Molecular Theory of Matter which states that matter of 
all kinds is composed of very small particles called mole- 
cules (see Art. 6), is a familiar example of a theory. 

A theory becomes a law when itmay be definitely proved. 
Many laws are expressed in mathematical language, 
e.g., the law of gravitation. (See Art. 88.) Many of 
the laws of physics are illustrated by laboratory experi- 
ments, which show in a simple way just what the law 
means. 

Exercises 

Explain what is meant by the following terms and expressions: 
i. Common knowledge. 

2. Scientific knowledge. 

3. Science. 

4. Topics in physics. 

5. Scientific habit of thought. 

6. Value of relating new ideas to former experiences. 

7. Hypothesis. 

8. Theory. 

9. Law. 



4 PHYSICS 

(2) The States of Matter 

4. Physics Defined. In the study of any science or 
field of knowledge, it is helpful to have a basis for grouping 
or classifying the facts studied. In physics we are to 
study the objects, forces, and changes about us, to under- 
stand them and their relations to one another. Accord- 
ingly, physics, dealing with the material world about us, 
is often denned as the science of matter and energy, matter 
being anything that occupies space and energy the capacity 
for doing work. This definition of physics while not 
strictly accurate is sufficiently comprehensive for our 
present purpose. 

5. The Three States of Matter. Our bodies are matter 
since they occupy space. Further, they possess energy 
since they are able to do work. In beginning the study 
of physics it will simplify our work if we study one of 
these topics before the other. We will therefore begin 
with matter and consider first its three states. 

Some bodies are solid; as ice, iron, wax. Others are 
liquid; as water, mercury, oil. Still others are in the state 
of gas; as steam, air, and illuminating gas. Further we 
notice that the same substance may be found in any one 
of the three states. For example water may be either ice, 
water or steam; that is, either a solid, a liquid, or a gas. 

Most persons have heard of liquid air and possibly some 
know of ice air, i.e., air cooled until it not only liquefies, 
but is solidified. On the other hand, iron may.be melted 
and, if heated hot enough, may be turned into iron vapor. 
In fact most substances by heating or cooling sufficiently 
may be changed into any one of the three states. 

Before denning the three states, let us consider the 
structure of matter. This may help us to answer the 
question: How is it possible to change a hard solid, such 



INTRODUCTION AND MEASUREMENT 5 

as ice, into a liquid, water, and then into an invisible gas 
like steam?. This is explained by the molecular theory 
of matter. I 

6. The Molecular Theory of Matter. It is believed 
that all bodies are made up of very small particles called 
molecules, and that these instead of being packed tightly 
together like square packages in a box, are, strange as it 
may seem, very loosely packed even in solids and do not 
permanently touch their neighbors. The size of these 
molecules is so minute that it has been estimated that if 
a drop of water could be magnified to the size of the earth, 

* the molecules magnified in the same proportion would be in 
size between a baseball and a football. The air and all 
other gases are believed to be made up of molecules in 
rapid motion, striking and rebounding continually from 
one another and from any objects in contact with the 
gas. 

7. States of Matter Defined. These ideas of the struc- 
ture of matter assist us in understanding the following 
definitions: A solid is that state of matter in which the 
molecules strongly cling together and tend to keep the same 
relative positions. (This of course follows from the ten- 
dency of a solid to retain a definite form.) A liquid is 
that state of matter in which the molecules tend to cling 
together yet move about freely. Hence a liquid takes the 
form of any vessel in which it is placed. A gas is that 
state of matter in which the molecules move about freely 
and tend to separate indefinitely. Hence a gas will fill 
any space in which it is placed. 

8. Effect of Heat on Matter. It is further believed that 
when a body is heated, that the action really consists in 
making its molecules move or vibrate faster and faster 
as the heating progresses. This increase of motion causes 
the molecules to push apart from one another and this 




6 PHYSICS 

separation of the molecules causes an expansion of the 
body whether it be solid, liquid, or gas. Fig. i shows 
the expansion of air in an air thermometer. 
Fig. 2 shows the expansion of a solid on 
heating. 

9. Physical and Chemical Changes. 
A change of state such as the freezing 
or boiling of water is called a physical 
change, for this change has not affected 
the identity of the substance. It is water 
even though it has become solid or 
gaseous. Heating a platinum wire red 
hot is also a physical change for the wire 
on cooling is found to be the same sub- 
stance as before. Further if salt or sugar 
be dissolved in water the act of solution 
is also a physical change since the identical 
substance (salt or sugar) is in the solu- 
tion and may be obtained by evaporating the water. 

If some sugar, however, is heated strongly, say in a 
test-tube, it is found to blacken, some water is driven off 



Fig. i. When 
the bulb is 
heated, the air 
within expands 
forcing down the 
water in the tube. 



C^mC 



3 



(a) (b) 

Fig. 2 (a) represents a straight bar made of a strip of brass and a 
strip of iron riveted together and attached to a handle. Upon heating 
the compound bar in a gas flame, the brass expands faster than the iron 
causing the bar to bend toward the latter as in Fig. 2 (b). 

and on cooling some black charcoal is found in the tube 
instead of the sugar. This action which has resulted in a 
change in the nature of the substance treated is called a 
chemical change. To illustrate further, if some magnesium 
wire is heated strongly in a flame, it burns, giving off an 
intense light and when it cools one finds it changed to a 
light powdery substance like ashes. Chemical changes, 



INTRODUCTION AND MEASUREMENT 7 

or those that change the nature of the substance affected, 
are studied in chemistry. In physics we have to do only 
with physical changes, that is, with those changes that 
do not affect the nature of the substance. 

Important Topics 

1. Physics defined. 

2. The three states of matter; solid, liquid, gas. 

3. Molecular theory of matter. 

4. Physical and chemical changes. 

Exercises 

Write out in your own words your understanding of: 

1. The structure of matter. 

2. Some of the differences between solids, liquids, and gases. 

3. How to change solids to liquids and gases and vice versa. 

4. The reason for the changes of size of a body on heating. 

5. Why cooling a gas tends to change it to a liquid or a solid. 

6. The actual size of molecules. 

Which of the following changes are chemical and which 
physical ? 
Give reasons. 

1. Melting of ice. 

2. Burning of a candle. 

3. Production of steam. 

4. Falling of a weight. 

5. Drying of clothes. 

6. Making an iron casting 

7. Decay of vegetables. 

8. Sprouting of seeds. 

9. Flying an aeroplane. 

10. Growth of a plant. 

11. Grinding of grain. 

12. Sawing a board. 

13. Pulverizing stone. 

14. Making toast. 

15. Sweetening tea or coffee with sugar. 

16. Burning wood or gas. 



PHYSICS 



(3) The Metric System 

10. The Metric System. In order to study the three 
states of matter with sufficient exactness it is necessary 
to employ a system of measurement. The system univer- 
sally employed by scientists is called The Metric System. 
In many respects it is the most convenient for all purposes. 
Every student should therefore become familiar with it 
and learn to use it. At the present time, not only do scien- 
tists everywhere use it, but many countries have adopted 
it and use it in common measurements. It was legalized 
in the United States in 1866. The metric system was 
originated by the French Academy of Sciences during the 
latter part of the 18th century. There were so many 
different systems" of weights and measures in use, each 
country having a system of its own, that commerce was 
much hindered. It was therefore decided to make a sys- 
tem based upon scientific principles. The length of the 
earth's quadrant passing from the equator to the pole 
was determined by surveying and computation. One- 
ten-millionth of this distance was selected as the unit of 
length and called a meter. Accurate copies of this meter 
were made and preserved as standards. 

Later surveys have shown that the original determina- 
tion of the earth's quadrant was not strictly accurate; so 
that after all the meter is not exactly one-ten -millionth of 
the earth's quadrant. 

11. The Standard Meter. The standard unit of length 
in the metric system is the meter. It is the distance, at 
the temperature of melting ice, between two transverse 
parallel lines ruled on a bar of platinum (see Fig. 3), which 



INTRODUCTION AND MEASUREMENT 9 

is kept in the Palace of the Archives in Paris. Accurate 
copies of this and other metric standards are also kept at 
the Bureau of Standards at Washington, 
D. C. Fig. 4 shows the relation between 
the inch and the centimeter (one-hundredth 
of a meter). 

12. Units and Tables in the Metric 
System. The metric unit of area commonly- 
used in physics is the square centimeter. 

The standard unit of volume or capacity . 

it- T 1 1 e FlG - 3- The 

is the liter. It is a cube one-tenth of a standard meter. 

meter on each edge. It is equal to 1.057 

quarts. It corresponds, therefore, to the quart in English 

measure. 



CENTIMETER 

12 3 4 5 




i.iii.li.mJmiljLiil 


1 mi l,i ml i,i 11 J uiij 1 


jiJiijilniilii 


1,1 In 1,1 kmju ii,l 1,1,1 iJjuilJU 


1 1 1 1 1 1 1 1 1 1 ] 

INCH 


I i|Ul|M 1 Ml 
1 


i|iiiii|i| 
2 


i|!|l| i|ih i|i|l|i 
3 



Fig. 4. Centimeter and inch scales. 

The standard unit of mass is the kilogram. It is the 
mass of 1 liter of pure water at the temperature of its 
greatest density, 4C. or 39.2 # F. 

The three principal units of the metric system, the 
meter, the liter, and the kilogram, are related to one another 
in a simple manner, since the liter is a cube one-tenth of 
a meter in each dimension and the kilogram is the mass 
of a liter of water. (See Fig. 5.) > 

The metric system is a decimal system that is, one unit 
is related to another unit in the ratio of ten or of some 
power of ten. This is indicated by the following 
tables: 



IO PHYSICS 

Metric Table of Length 

10 millimeters (mm.) equal i centimeter. 

10 centimeters (cm.) equal i decimeter. 

10 decimeters (dm.) equal i meter. 

10 meters (m.) equal i dekameter. 

10 dekameters (Dm.) equal i hectometer. 

10 hectometers (hm.) equal i kilometer. 

10 kilometers (km.) equal i myriameter. 

The measures commonly used are the centimeter, meter and kilo- 
meter. 

Metric Table of Mass (or Weight) 

10 milligrams (mg.) equal i centigram. 

10 centigrams (eg.) equal i decigram. 

10 decigrams (dg.) equal i gram. 

10 grams (g.) equal i dekagram 

10 dekagrams (Dg.) equal i hectogram. 

10 hectograms (hg.) equal i kilogram. 

10 kilograms (kg.) equal i myriagram. 

The masses commonly used are the milligram, gram and kilogram. 

Notice in these tables the similarity to 10 mills equal i cent, 10 
cents equal i dime, 10 dimes equal i dollar, in the table of United 
States money. 

Other tables in the metric system are built upon the same plan. 
Learn the prefixes in order thus: milli, centi, deci, deka, hecto, kilo, 
myria. The first three prefixes are Latin numerals and represent 
divisions of the unit. The last four are Greek numerals and repre- 
sent multiples. In these tables, milli means Kooo> centi means 
i/ioo, deci means i/io, deka means 10, hecto, ioo, kilo, iooo, myria, 
10,000. Two other prefixes are sometimes used, micro which means 
1/1,000,000; as microfarad or microvolt, and meg which means 
1,000,006, as megohm meaning 1,000,000 ohms. 

13. Advantages of the Metric System. First, it is a 
decimal system; second, the same form and prefixes are 
used in every table; third, the standards of length (meter), 
volume (liter), and mass (kilogram) bear a simple relation 



INTRODUCTION AND MEASUREMENT 



II 



to one another. This simple relation between the three 
standard units may be given thus: first, the liter is a cubic 
decimeter, and second, the kilogram is the mass of a liter 
of water. (See Fig. 5 ) Since the liter is a cubic deci- 




Fig. 5. One liter of the water has a mass of one kilogram. 



meter, the length of one side is 10 cm. The liter there- 
fore holds 1000 ccm. (10 X 10 X 10). Therefore, 1 liter 
= 1 cu. dm. = 1000 ccm. and since 1 liter of water has a 
mass of 1 kg. or 1000 g., then 1000 ccm. of water has a mass 
of 1000 g., or 1 ccm. of water has a mass of 1 g. 

The following table of equivalents gives the relation 
between the most common English and metric units. 
Those marked (*) should be memorized. 



(*) 


1 meter = 39.37 inches. 




1 cu. in. 


= 16.387 ccm. 


(*) 


1 inch = 2.54 cm. 




1 cu. ft. 


= 28315 cm. 




1 foot = 30.48 cm. 




1 cu. m. 


= 1.308 cu. yd 




1 mile = 1.609 km. 


(*) 


1 liter 


= 1.057 qt. 




1 sq. in. = 6.45 sq. cm. 


(*) 


1 kg. 


= 2.204 lbs. 




1 sq. cm. = .155 sq. in. 




1 g. 


= 15.44 grains 




1 sq. m. = 1. 196 sq. yd. 




1 lb. 


= 0.4536 kg. 




1 acre = 0.405 ha. 




1 oz. 


= 28.35 g- 




1 hectare = 2.45 acres. 




1 g. 


= 0.0353 oz. 



The c. g. s. system. Scientists have devised a plan for express- 
ing any measurement in terms of what are called the three funda- 



1 2 PHYSICS 

menial units of length, mass, and time. The units used are the centi- 
meter, the gram and the second. Whenever a measurement has been 
reduced to its equivalent in terms of these units, it is said to be 
expressed in C. G. S. units. 

Important Topics 

i. The metric system; how originated. 

2. Units; meter, liter, kilogram. 

3. Metric tables. 

4. Advantages of the metric system. 

5. Equivalents. 

6. The C. G. S. system. 

Exercises 

1. Which is cheaper, milk at 8 cents a quart or 8 cents a liter? 
Why? 

2. Which is more expensive, cloth at $1.00 a yard or at $1.00 a 
meter? Why? 

3. Which is a better bargain, sugar at 5 cents a pound or 1 1 cents 
a kilogram? Why? 

4. Express in centimeters the height of a boy 5 ft. 6 in. tall. 

5. What is the length of this page in centimeters? In inches? 

6. What is the mass of a liter of water? Of 500 ccm. ? Of 1 ccm. ? 

7. From Chicago to New York is 940 miles. Express in kilometers. 

8. A 10-gallon can of milk contains how many liters? 

9. What will 100 meters of cloth cost at 10 cents a yard? 

10. What will 4 kg. of beef cost at 15 cents a pound? 

11. What will 5H lbs. of mutton cost at 40 cents a kilogram? 

12. How can you change the state of a body? Give three methods. 

13. Correct the statement 1 ccm. = ig. 

14. How many liters in 32 quarts? 



CHAPTER II 
MOLECULAR FORCES AND MOTIONS 

(i) Evidences of Molecular Motion in Gases 

14. Size of Molecules. The difference between solids, 
liquids, and gases has been explained as due to the dif- 
ferent behavior of molecules in the three states of matter. 
That is, in solids they cling together, in liquids they move 
freely, and in gases they separate. At this time we are 
to consider the evidences of molecular motion in gases. 
It must be kept in mind that molecules are exceedingly 
small. It has been said that if a bottle containing about 
1 ccm. of ordinary air has pierced in it a minute opening 
so that 100,000,000 molecules (a number nearly equal to 
the population of the United States) pass out every second, 
it would take, not minutes or hours, but nearly 9000 
years for all of the molecules to escape. The number of 
molecules in 1 ccm. of air at oC. and 76 cm. pressure has 
been calculated by Professor Rutherford to be 2.7 X io 19 . 
It is evident that such minute particles cannot be seen 
or handled as individuals. We must judge of their size 
and action by the results obtained from experiments. 

15. Diffusion of Gases. One line of evidence which 
indicates that a gas consists of moving particles is the 
rapidity with which a gas having a strong odor penetrates 
to all parts of a room. For example, if illuminating gas 
is escaping it soon diffuses and is noticed throughout the 
room. In fact, the common experience of the diffusion 
of gases having a strong odor is such that we promptly 

13 



14 



PHYSICS 



recognize that it is due to motion of some kind. The gas 
having the odor consists of little particles that are con- 
tinually hitting their neighbors and are being struck and 
buffeted in turn until the individual molecules are widely 
scattered. When cabbage is boiled in the kitchen soon 
all in the house know it. Other illustrations of the diffu- 
sion of gases will occur to anyone from personal experience, 
such for instance as the pleas- 
ing odor from a field of clover 
in bloom. 

The following experiment 
illustrates the rapid diffusion 
of gases. 





Fig. 6a. Diffusion of gases. 



Fig. 6b. Effusion of gases. 



Take two tumblers (see Fig. 6a), wet the inside of one with a few 
drops of strong ammonia water and the other with a little hydro- 
chloric acid. Cover each with a sheet of clean paper. Nothing can 
now be seen in either tumbler. Invert the second one over the first 
with the paper between, placing them so that the edges will match. 
On removing the paper it is noticed that both tumblers are quickly 
filled with a cloud of finely divided particles, the two substances hav- 
ing united chemically to form a new substance, ammonium chloride. 

On account of their small size, molecules of air readily 
pass through porous solids, cloth, unglazed earthenware, 
etc. The following experiment shows this fact strikingly. 
(See Fig. 6b.) 



MOLECULAR FORCES AND MOTIONS 1 5 

A flask containing water is closed by a rubber stopper through 
which pass the stem of a glass funnel and a bent glass tube that has 
been drawn out to a small opening (/). The funnel has cemented 
in its top an inverted porous clay jar (C), over the top of the 
latter is placed a beaker (23). A piece of flexible rubber tubing 
(H) leading from a hydrogen generator is brought up to the top of 
the space between the jar and the beaker. When hydrogen gas 
is allowed to flow into the space between C and B, the level of the 
water in W is seen to lower and a stream of water runs out at J 
spurting up into the air. 

On stopping the flow of hydrogen and removing B, the water 
falls rapidly in / and bubbles of air are seen to enter the water 
from the tube. (The foregoing steps may be repeated as often as 
desired). 

This experiment illustrates the fact that the molecules of some 
gases move faster than those of some other gases. Hydrogen mole- 
cules are found to move about four times as fast as air molecules. 
Hence, while both air and hydrogen molecules are at first going in 
opposite directions through the walls of C, the hydrogen goes in 
much faster than the air comes out. In consequence it accumulates, 
creates pressure, and drives down the water in W and out at J. On 
removing B, the hydrogen within the porous cup comes out much 
faster than the air reenters. This lessens the pressure within, so 
that air rushes in through J. This experiment demonstrates not 
only the fact of molecular motion in gases but also that molecules 
of hydrogen move much faster than those of air. (This experiment 
will work with illuminating gas but not so strikingly.) 

Careful experiments have shown that the speed of 
ordinary air molecules is 445 meters or 1460 ft. per second; 
while hydrogen molecules move at the rate of 1 700 meters 
or 5575 ft. or more than a mile per second. 

16. Expansion of Gases. Gases also possess the prop- 
erty of indefinite expansion, that is, if a small quantity of 
gas is placed in a vacuum, the gas will expand immediately 
to fill the entire space uniformly. This is shown by an 
experiment with the air pump. On raising the piston the 
air follows instantly to fill up the space under it. As 



1 6 PIIYSICS 



the air is removed from the receiver of an air pump the air 
remaining is uniformly distributed within. 

17. How Gases Exert Pressure. It is further found 
that air under ordinary conditions exerts a pressure of 
about 15 lbs. to the square inch. In an automobile tire 
the pressure may be 90 lbs. and in a steam boiler it may 
be 200 lbs. or more to the square inch. 

How is the pressure produced? The molecules are not 
packed together solidly in a gas, for when steam changes to 
water it shrinks to about }<i600 01 " its former volume. 
Air diminishes to about 3^00 of its volume on changing to 
liquid air. The pressure of a gas is not due then to the 
gas filling all of the space in which it acts, but is due rather 
to the motion of the molecules. The blow of a single mole- 
cule is imperceptible, but when multitudes of molecules 
strike against a surface their combined effect is consider- 
able. In fact, this action is known to produce the 
pressure that a gas exerts against the walls of a con- 
taining vessel. Naturally if we compress twice as much 
gas into a given space there will be twice as many 
molecules striking in a given time, which will give twice 
as much pressure. 

If gas is heated, it is found that the heat will cause a 
swifter motion of the molecules. This will also make the 
molecules strike harder and hence cause the gas to expand 
or exert more pressure. 

17a. Brownian Movements. Direct photographic 
evidence of the motion of molecules in gases has been 
obtained by studying the behavior of minute drops of 
oil suspended in stagnant air. Such drops instead of 
being at rest are constantly dancing about as if they 
were continually receiving blows from many directions. 
These motions have been called Brownian Movements 
(see Fig. 7). 



MOLECULAR FORCES AND MOTIONS 



17 



It has been proved that these movements are due to 
the blows that these small drops receive from the swiftly- 
moving molecules of the gas about them. If the drops 
are made smaller or the gas more dense, the movements 
increase in intensity. These effects are especially marked 
at a pressure of 0.01 of an atmosphere. 




v .. W^i 



Fig. 7. Photograph of Brownian movement. This record is pre- 
pared by the aid of Siedentopf's ultra-microscope and a plate moving 
uniformly across the field from left to right. 



Important Topics 

It is assumed that air and all gases are made up of molecules in 
rapid motion; that this motion is dependent upon temperature and 
pressure. Evidence of this is shown by (a) diffusion, (b) expansion, 
(c) pressure. Brownian Movements. 



Questions 

1. What is the molecular (kinetic) theory of gases? 

2. What three kinds of evidence help to confirm the theory? 

3. What have you seen that seems to show that a gas consists of 
molecules in motion? 

4. How many meters long is a 10-ft. pole? 

5. A 50-kg. boy weighs how many pounds? 

6. What are three advantages of the metric system? 

7. What will 12 qts. of milk cost at 8 cents a liter? 

8. A cube 1 meter each way will contain how many cubic centi- 
meters? How many liters? What will a cubic meter of water 
weigh? 



1 8 PHYSICS 

(2) Molecular Motion in Liquids 

18. Diffusion of Liquids. From the evidence given in 
Arts. 14-17, (a) of diffusion of odors, (b) of the continued 
expansion of air in the air pump, and (c) of the pressure 
exerted by a gas in all directions, one may realize without 
difficulty that a gas consists oj small particles in rapid 
motion. Let us now consider some of the evidence of 
molecular motion in liquids. If a little vinegar is placed 
in a pail of water, all of the water will soon taste sour. 
A lump of sugar in a cup of tea will sweeten the entire 
contents. This action is somewhat similar to the diffusion 
of gases but it takes place much more slowly. It is there- 
fore believed that the motion of liquid molecules is 
much slower than that of gas molecules. 

Again, if a dish of water is left standing in the open air 
in fine weather, within a few days the dish will become 
dry though no one has taken anything from it. We say 
the water has evaporated. What was liquid is now vapor. 
If we were to observe carefully any dish of water we would 
find that it continually loses weight on dry days. That is, 
there is a constant movement of the molecules of water 
into the air. This movement of the molecules is explained 
as follows. There appear to be in the dish of water some 
molecules that by moving back and forth acquire a greater 
velocity than their neighbors ; when these reach the sur- 
face of the liquid, some vibration or movement sends them 
flying into the air above. They are now vapor or gas 
molecules, flying, striking, and rebounding like the air 
molecules. Sometimes on rebounding, the water mole- 
cules get back into the water again. This is especially 
apt to happen when the air is damp, i.e., when it contains 
many water molecules. Sometimes the air over a dish 
becomes saturated, as in the upper part of a corked bottle 



MOLECULAR FORCES AND MOTIONS 



19 



containing water. Although molecules are continually 
leaving the surface of the water they cannot escape from 
the bottle, so in time as many molecules must return 
to the water from the space above as leave the water in 
the same time. When this condition exists, the air above 
the water is said to be saturated. On 
very damp days the air is often satur- 
ated. The explanation above shows 
why wet clothes dry so slowly on such 
a day (See Arts. 166-7 on Saturation.) 

19. Cooling Effect of Evaporation. 
We have seen that warming a gas 
increases its volume. This expansion 
is due to the increased motion of the 
warmed molecules. Now the molecules 
that escape from a liquid when it 
evaporates are naturally the fastest 
moving ones, i.e., the hottest ones. The 
molecules remaining are the slower 
moving ones or colder molecules. The 
liquid therefore becomes colder as it 
evaporates, unless it is heated. This 
explains why water evaporating on 
the surface of our bodies cools us. In 
evaporating, the water is continually 
losing its warm, fast moving molecules. 
The cooling effect of evaporation is 
therefore an evidence of molecular 
motion in liquids. 

20. Osmosis. If two liquids are separated by a mem- 
brane or porous partition, they tend to pass through and 
mix. This action is called osmose, or osmosis. 

Such a movement of liquid molecules in osmosis may be illus- 
trated by filling a beet or carrot that has had its interior cut out 




Fig. 8. Osmosis 
shown by carrot 
placed in water. 



20 PHYSICS 

to form a circular opening (see Fig. 8) with a thick syrup. The 
opening is then closed at the top with a rubber stopper through 
which passes a long glass tube. 

If the carrot is immersed in water, as in Fig. 8, a movement of 
water through the porous wall to the interior begins at once. Here, 
as in the experiment of the hydrogen and air passing through the 
porous cup, the lighter fluid moves faster. The water collecting in 
the carrot rises in the tube. This action of liquids passing through 
porous partitions and mingling is called osmosis. 

Gases and liquids are alike in that each will flow. Each 
is therefore called a fluid. Sometimes there is much re- 
sistance to the flow of a liquid as in molasses. This 
resistance is called viscosity. Alcohol and gasoline have 
little viscosity. They are limpid or mobile Air also has 
some viscosity. For instance, a stream of air always drags 
some of the surrounding air along with it. 

Important Topics 

1. Liquids behave as if they were composed of small particles in 
motion. 

2. This is shown by (i) Diffusion, (2) Solution, (3) Evaporation, 
(4) Expansion, (5) Osmosis. 

Exercises 

1. Give an example or illustration of each of the five evidences of 
molecular motion in liquids. 

2. When is air saturated? What is the explanation? 

3. Why does warming a liquid increase its rate of evaporation? 

4. Air molecules are in rapid motion in all directions. Do they 
enter a liquid with a surface exposed to the air? Give reason. 

5. What are some of the' inconveniences of living in a saturated 
atmosphere? 

6. Fish require oxygen. How is it obtained? 



molecular forces and motions 21 

(3) Molecular Forces in Liquids 
21. Cohesion and Adhesion. In liquids "the molecules 
move about freely yet tend to cling together." This 
tendency of molecules to cling together which is not 
noticeable in gases is characteristic of liquids and especially 
of solids. It is the cause of the viscosity mentioned in 
the previous section and is readily detected in a variety 
of ways. For instance, not only do liquid molecules 
cling together to form drops and streams, but they cling 
to the molecules of solids as well, as is shown by the wet 
surface of an object that has been dipped in water. The 
attraction of like molecules for one another is called 
cohesion, while the attraction of unlike molecules is called 
adhesion^ although the force is the same whether the mole- 
cules are alike or unlike. It is the former that causes 
drops of water to form and that holds iron, copper, and 
other solids so rigidly together. The adhesion of glue to 
other objects is well known. Paint also "sticks" well. 
Sometimes the " joint " where two boards are glued together 
is stronger than the board itself. The force of attraction 
between molecules has been stud- 
led carefully. 1 he attraction acts fc 

only through very short distances. 
The attraction even in liquids is 
considerable and may be measured. 
The cohesion of water may be 
shown by an experiment where 
the force required to pull a glass 



plate from the surface of water FlG - 9 -~ T 1 he w * ter is 

pulled apart. 

is measured. 

Take a beam balance and suspend from one arm a circular glass 
plate, Fig. 9. Weigh the plate and its support. Adjust the glass 
plate so that it hangs horizontally and just touches the surface of 
clean water, the under side being completely wet. Now find what 
additional weight is required to raise the glass plate from the water. 



22 



PHYSICS 



Just as the plate comes from the water its under side 
is found to be wet. That is, the water was pulled apart, 
and the plate was not pulled from the water. The co- 
hesion of the water to itself is not so strong as its adhesion 
to the glass. 

The cohesion of liquids is further shown by the form a 
drop of liquid tends to take when left to itself. This is 
readily seen in small drops of liquids. The spherical 
shape of drops of water or mercury is an example. A 
mixture of alcohol and water in proper proportions will 
just support olive oil within it. By carefully dropping 
olive oil from a pipette into such a mixture, a drop of the 
oil, an inch or more in diameter suspended in the liquid, 
may be formed. It is best to use a bottle with plane or 
flat sides, for if a round bottle is used, the sphere of oil will 
appear flattened. 





Fig. io a. Fig. io b. 

Figs, io a and b. Surface tension of a liquid film. 

22. Surface Tension. The cohesion of liquids is also 
indicated by the tendency of films to assume the smallest 
possible surface. Soap bubble films show this readily. 
Fig. io a represents a circular wire form holding a film 
in which floats a loop of thread. The tension of the 



MOLECULAR FORCES AND MOTIONS 



23 



film is shown in Fig. 10 & by the circular form of the loop 
after the film within it has been pierecd by a hot wire, 
Fig. 11 shows a rectangular wire form with a "rider." 
The tension in the film draws the rider forward. 

A soap bubble takes its 
spherical shape because 
this form holds the con- 
fined air within the 





Fig. 



1 1 . The rider is drawn for- 
ward. 



Fig. 12. Surface tension causes 
the pointed shape. 



*S 



ssssfi' 



smallest possible surface. A drop of liquid is spherical 
for the same reason. Many illustrations of the tension 
in films may be given. Users of water colors notice that 
a dry camePs-hair brush is bushy. (Fig. 12 A). When 
in water it is still bushy. (Fig. 12 B.) 
But when it is taken from the water 
and the excess is shaken from it, it is 
pointed as in Fig. 12 C. It is held to 
the pointed shape by the tension of 
the liquid film about the brush. 

The surface of water acts as if covered by a film which 
coheres more strongly than the water beneath it. This is 
shown by the fact that a steel needle or a thin strip of 
metal may be floated upon the surface of water. It is sup- 
ported by the surface film. (See Fig. 13.) If the film 
breaks the needle sinks. This film also supports the little 
water bugs seen running over the surface of a quiet pond in 



Fig. 13. A needle 
depresses the surface 
when floating. 



24 



PHYSICS 



summer. The surface film is stronger in some liquids than 
in others. This may be shown by taking water, colored 
so that it can be seen, placing a thin layer of it on a white 
surface and dropping alcohol upon it. Wherever the 
alcohol drops, the water is seen to pull away from it, 
leaving a bare space over which the alcohol has been spread. 
This indicates that the alcohol has the weaker film. The 
film oj greasy benzine is stronger than the film of the pure 
material. If one wishes to remove a grease spot and 
places pure benzine at the center of the spot, the stronger 
film of the greasy liquid will pull away from the pure 
benzine, and spread out, making a larger spot than before, 
while if pure benzine is placed around the grease spot, the 
greasy liquid at the center pulls away from the pure ben- 
zine, drawing more and more to the center, where it may 
be wiped up and the grease entirely removed. 




ooooooo 



Fig. 14. The molecule at A is held differently from one within the liquid. 

23. Explanation of the Surface Film. Beneath the sur- 
face of a liquid each molecule is attracted by all the other 
molecules around it. It is attracted equally in all direc- 
tions. Consequently the interior molecules move very 
easily over each other in any direction. A molecule at the 
surface, as at A, Fig. 14, is not attracted upward by other 
liquid molecules. Its freedom of motion is thereby 
hindered with the result that a molecule at the surface 



MOLECULAR FORCES AND MOTIONS 



25 



;-- 



^i Tt u " 1 ' ' " ' ' 1 ' > u . maegj 



Fig. 



IS- 



Capillary attraction 
in tubes. 



behaves differently from one beneath the surface. The 
surface molecules act as if they form an elastic skin or 
membrane upon the liquid surface. 

24. Capillarity. A striking action of the surface film 
of a liquid is seen in the rise of liquids in tubes of small 
bore when the liquid wets them. If the liquid does not wet 
the tube, as when mercury is placed in glass, the liquid is 
depressed. It is found in gen- 
eral that : Liquids rise in capil- 
lary tubes when they wet them 
and are depressed in tubes 
which they do not wet; the 
smaller the diameter of the tube 
the greater the change of level. 
(See Fig. 15.) This action is 
explained as follows : The mole- 
cules of a liquid have an at- 
traction for each other and also 

for the sides of a tube. The former is called "cohesion 
for itself," the latter is called "adhesion for the sides 
of the containing vessel." If the cohesion for itself is 
greater than the adhesion for the side of the containing 
vessel, the liquid is pulled away from the side and is 
depressed. If the adhesion is greater, the liquid is ele- 
vated. This action is called "capillary action" from 
the Latin word (capillus) signifying hair, since it shows 
best in fine hairlike tubes. 

There are many common illustrations of capillary action : 
oil rising in a wick; water rising in a towel or through 
clothes; ink in a blotter, etc. The minute spaces be- 
tween the fibers composing these objects act as fine 
tubes. If cloth is treated with a preparation which pre- 
vents water from adhering to its fibers, the material 
will not be wet when water is poured upon it, because 



26 PHYSICS 

the water will not run in between the fibers; a surface 
film spreads over the cloth so that no water enters it. 
Cravenette cloth has been treated ,in this way and hence is 
waterproof. 

The action of this film may be shown by the following experiment. 
Dip a sieve of fine copper gauze in melted paraffin, thus coating 
each wire so that water will not adhere to it. Water may now be 
poured into the sieve, if a piece of paper is first laid in it to break 
the force of the water. On carefully removing the paper the surface 
film of the water will prevent the passage of the water through 
the sieve. 

25. Capillary Action in Soils. The distribution of 
moisture in the soil depends largely upon capillary action. 
When the soil is compact the minute spaces between the 
soil particles act as capillary tubes, thus aiding the water 
to rise to the surface. As the water evaporates from the 
surface more of it rises by capillary action from the damper 
soil below. Keeping the soil loose by cultivation, makes 
the spaces between the particles too large for much capil- 
lary action, thus the moisture is largely prevented from 
rising to the surface. 

In the semi-arid regions of the West "dry farming" 
is successfully practised. This consists in keeping the sur- 
face covered with a "dust mulch" produced by frequent 
cultivation. In this way the moisture is kept below the 
surface, where it can be utilized during the hot dry sum- 
mer by the roots of growing plants. 

Important Topics 

1. Attractive forces between liquid molecules. 

2. Cohesion (like molecules); adhesion (unlike molecules). 

3. Special effects of this force are classified as (a) capillary action, 
and (b) surface tension. 



MOLECULAR FORCES AND MOTIONS 27 

Exercises 

1. What evidence of capillary action have you seen outside of the 
laboratory? 

2. What is the explanation for capillary action? 

3. Where are surface films found? 

4. What are three common effects of surface films? 

5. Explain why cravenette cloth sheds water. 

6. If a circular glass disc 10 cm. in diameter requires 50 grams of 
force to draw it from the water, what is the cohesion of water 
per square centimeter? 

7. What is the weight in grams of 1 ccm. of water? of a liter of 
water? 

8. Name five examples of adhesion to be found in your home. 

9. Under what conditions will a liquid wet a solid and spread over 
it. 

10. When will it form in drops on the surface? 
n. Explain the proper procedure for removing a grease spot with 
benzine. 

12. What difference is there between a liquid and a fluid? 

13. Why cannot a "soap bubble" be blown from pure water? 

14. Which are larger, the molecules of steam or those of water? 
Why? 

15. Why is' the ground likely to be damp under a stone or board 
when it is dry all around? 

16. Why does any liquid in falling through the air assume the 
globule form? 

17. Give three examples of capillary attraction found in the home. 
Three out of doors. 

18. Why does cultivation of the soil prevent rapid evaporation 
of water from the ground? 

(4) Evidences of Molecular Forces in Liquids and 

Solids 

26. Solutions. A crystal of potassium permanganate 
is placed in a liter of water. It soon dissolves and on shak- 
ing the flask each portion of the liquid is seen to be colored 
red. The dissolving of the permanganate is an illustra- 



28 PHYSICS 

tion of the attraction of the molecules of water for the 
molecules of the permanganate. We are familiar with this 
action in the seasoning of food with salt and sweetening 
with sugar. 

Water will dissolve many substances, but in varying 
degrees, i.e., of some it will dissolve much, of others, little, 
and some not at all. Further, different liquids have differ- 
ent solvent powers. Alcohol will dissolve resin and shellac, 
but it will not dissolve gum arabic, which is soluble in 
water. Benzine dissolves grease. Beeswax is not dis- 
solved by water, alcohol or benzine, but is soluble in 
turpentine. 

It is found that the temperature of the liquid has a 
marked effect upon the amount of substance that will 
dissolve. This is an indication that the motions of the 
molecules are effective in solution. It appears that dis- 
solving a solid is in some respects similar to evaporation, 
and just as at higher temperatures more of the liquid 
evaporates, because more of the molecules will escape from 
the liquid into the air above, so at higher temperatures, 
more molecules of a solid will detach themselves through 
greater vibration and will move into the liquid. 

Further, just as an evaporating liquid may saturate 
the space above it so that any escape of molecules is 
balanced by those returning, so with a dissolving solid, the 
liquid may become saturated so that the solution of more 
of the solid is balanced by the return of the molecules 
from the liquid to the solid condition. 

27. Crystals and Crystallization. This return from 
the liquid to the solid state, of molecules that are in solu- 
tion, is especially noticeable when the solution is cooling 
or evaporating and hence is losing its capacity to hold so 
much of the solid. On returning to the solid, the mole- 
cules attach themselves in a definite manner to the solid 



MOLECULAR FORCES AND MOTIONS 20. 

portion, building up regular solid forms. These regular 
forms are crystals. The action that forms them is called 
crystallization. 

Each substance seems to have its own peculiar form of 
crystal due to the manner in which the molecules attach 
themselves to those previously in place. The largest 
and most symmetrical crystals are those in which the 
molecules are deposited slowly with no disturbance of 
the liquid. Beautiful crystals of alum may be obtained 
by dissolving 25 g. of alum in 50 ccm. of hot water, hang- 
ing two or three threads in the solution and letting it 
stand over night. The thread fibers provide a foundation 
upon which crystals grow. . 

When a solution of a solid evaporates, the molecules of 
the liquid escape as a gas, the molecules of the solid remain 
accumulating as crystals. This principle has many uses: 

(a) sea water is purified by evaporating the water and 
condensing the vapor, which of course forms pure water. 

(b) Water is forced down to salt beds where it dissolves 
the salt. The brine is then raised and evaporated, leaving 
the salt in the evaporating pans. 

28. Absorption of Gases by Solids and Liquids. If a piece of 
heated charcoal is placed in a test-tube containing ammonia gas, 
inverted in mercury, the ammonia is seen to disappear, the mercury 
rising to take its place. The ammonia has been absorbed by the 
charcoal, the gas molecules clinging closely to the solid. The 
charcoal being very porous presents a large surface to the action of 
the gas. 

This experiment indicates that attraction exists beween 
gas molecules and other molecules. Many porous sub- 
stances have this power of absorbing gases. We have all 
noticed that butter has its flavor affected by substances 
placed near it. 

That liquids absorb gases is shown by slowly heating 



30 PHYSICS 

cold water in a beaker. Small bubbles of air form on the 
sides and rise before the boiling point is reached. Am- 
monia gas is readily absorbed in water, the bubbles dis- 
appearing almost as soon as they escape into the water 
from the end of the delivery tube. Household ammonia is 
simply a solution of ammonia gas in water. On warming 
the solution of ammonia the gas begins to pass off; thus, 
warming a liquid tends to drive off any gas dissolved in it. 
Soda water is made by forcing carbon dioxide gas into 
water under strong pressure. When placed in a vessel 
open to the air the pressure is lessened and part of the 
gas escapes. The dissolved gas gives the characteristic 
taste to the beverage. 

Important Topics 

i. The solution of solids is increased by heating. 

2. The solution of gases is decreased by heating. 

3. Pressure increases the quantity of gas that can be dissolved in a 
liquid. 

4. The attraction (cohesion) of molecules of a dissolved solid for 
each other is shown by crystallization. 

Exercises 

1. How do fish obtain oxygen for breathing? 

2. Why does warming water enable it to dissolve more of a salt? 

3. Why does warming water lessen the amount of a gas that will 
stay in solution? 

4. Will water absorb gases of strong odor? How do you know? 
"5. Name three solvents. Give a use for each. 

6. What liquids usually contain gases in solution? Name some 
uses for these dissolved gases. 

7. What is the weight of a cubic meter of water? 

8. Name three substances obtained by crystallization. 

9. How is maple sugar obtained? 
10. Name five crystalline substances. 



molecular forces and motions 3 1 

(5) Evidence of Molecular Forces in Solids 

29. Differences between Solids and Gases. In study- 
ing gases, it is seen that they behave as if they were 
composed of small particles in rapid motion, continually 
striking and rebounding, and separating to fill any space 
into which they are released. This action indicates that 
there is practically no attractive force between such 
molecules. 

Between the molecules of a solid, however, the forces 
of attraction are strong, as is shown by the fact that a 
solid often requires a great force to pull it apart; some, as 
steel and iron, show this property in a superlative degree, 
a high-grade steel rod i cm. in diameter requiring nearly 
9 tons to pull it apart. Tests show that the breaking 
strengths of such rods are directly proportional to their 
areas of cross-section. 
That is, twice the area _ t ifr fr 
has twice the breaking 
strength. 

30. Elasticity. 
Fully as important as 

a knowledge of the Fig. i 6 Elasticity of bending. 

breaking strengths of 

solids, is the knowledge of what happens when the forces 

used are not great enough to break the rods or wires. 

Take a wooden rod (as a meter stick) and clamp one end to the 
table top, as in Fig. 16. At the other end hang a weight. Fasten a 
wire to this end so that it projects but in front of a scale. Add suc- 
cessively several equal weights and note the position of the wire each 
time. Remove the weights in order, noting the positions as before. 
The rod will probably return to the first position. 

This simple experiment illustrates a characteristic of 
solids : that of changing shape when force is applied and of 




32 PHYSICS 

returning to the original shape when the force is removed. 
This property is called elasticity. 

Tests of elasticity are made by subjecting wire of dif- 
ferent materials but of the same dimensions to the same 
tension. The one changing least is said to have the great- 
est elastic force or elasticity. If greater forces are applied 
to the wire and then removed, one will finally be found 
that will permanently stretch the wire so that it will not 
return exactly to the former length. The wire has now 
passed its elastic limit and has been permanently stretched. 

Just as there are great differences between the elastic 
forces of different substances, so there are great differences 
in the limits of elasticity. In some substances the limit 
is reached with slight distortion, while others are perfectly 
elastic even when greatly stretched. India rubber is an 
example of a body having perfect elasticity through wide 
limits. Glass has great elastic force but its limit of elas- 
ticity is soon reached. Substances like India rubber may 
be said to have great " stretchability , " but little elastic 
force. In physics, elasticity refers to the elastic force 
rather than to ability to endure stretching. 

31. Kinds of Elasticity. Elasticity may be shown in 
four ways: compression, bending or flexure, extension or 
stretching, twisting or torsion. The first is illustrated by 
squeezing a rubber eraser, the second by an automobile 
spring, the third by the stretching of a rubber band, the 
fourth by the twisting and untwisting of a string by which 
a weight is suspended. 

There are two kinds of elasticity: (1) elasticity of form 
or shape; (2) elasticity of volume. Gases and liquids 
possess elasticity of volume, but not of shape, while solids 
may have both kinds. Gases and liquids are perfectly 
elastic because no matter how great pressure may be 
applied, as soon as the pressure is removed they regain 



MOLECULAR FORCES AND MOTIONS 33 

their former volume. No solid possesses perfect elas- 
ticity, because sooner or later the limit of elasticity will be 
reached. 

32. Hooke'sLaw. * Oh examining the successive move- 
ments of the end of the rod in Art. 30, we find that they 
are approximately equal. Carefully conducted experi- 
ments upon the elasticity of bodies have shown that the 
changes in shape are directly proportional to the forces 
applied, provided that the limit of elasticity is not reached. 
This relation, discovered by Robert Hooke, is sometimes 
expressed as* follows: " Within the limits of perfect elasticity, 
all changes of size or shape are directly proportional to the 
forces producing them." 

33. Molecular Forces and Molecular Motions. If a 
solid is compressed, on releasing the pressure the body 
regains its former shape if it has not been compressed too 
far. This indicates that at a given temperature the 
"molecules of a solid tend to remain at a fixed distance 
from each other, and resist any attempt to decrease or 
increase this distance." This raises the question, Why 
does not the cohesion pull the molecules tightly together 
so that compression would be impossible? The reason 
is that heat affects the size of solid bodies. On lowering 
the temperature, bodies do contract, for as soon as the 
temperature is lowered the vibration of the molecule is 
lessened. On raising the temperature the molecules are 
pushed farther apart. 

The size of a body, then, is the result of a balance of 
opposing forces. The attractive force between the mole- 
cules pulling them together is cohesion, while the force 
which pushes them apart is due to the motions of the 
molecules. Raising the temperature and thus increasing 

* A law is a statement of a constant mode of behavior. It is 
often expressed in mathematical language. 
3 



34 PHYSICS 

the motion causes expansion; lowering the temperature 
decreases the molecular motion and so causes contraction. 
If an outside force tries to pull the body apart or to com- 
press it this change of size is resisted by either cohesion or 
molecular motion. 

34. Properties of Matter. Many differences in the 
physical properties of solids are due to differences between 
the cohesive force of different kinds of molecules. In 
some substances, the attraction is such that they may be 
rolled out in very thin sheets. Gold is the best example of 
this, sheets being formed ^00,000 of an inch thick. This 
property is called malleability. In other substances the 
cohesion permits it to be drawn out into fine threads or 
wire. Glass and quartz are examples of this. This 
property is called ductility. In some, the cohesion make 
the substance excessively hard, so that it is difficult to 
work or scratch its surface. The diamond is the hardest 
substance known. Some substances are tough, others 
brittle. These are tested by the ability to withstand 
sudden shocks as the blow of a hammer. 

Important Topics 

1. Molecular forces in solids; (a) adhesion, (ft) cohesion. 

2. Elasticity, Hooke's Law. 

3. Contraction on cooling. 

4. Malleability, ductility, hardness, brittleness, etc. 

Exercises 

1. Give an illustration of Hooke's Law from your own experience. 

2. What devices make use of it? 

3. Do solids evaporate. Give reasons. 

4. When iron is welded, is cohesion or adhesion acting? 

5. When a tin basin is soldered, is cohesion or adhesion acting? 

6. Sometimes a spring is made more elastic by tempering and made 
soft by annealing. Look up the two terms. How is each 
accomplished ? 



MOLECULAR FORCES AND MOTIONS 35 

7. Review the definitions: solid, liquid, and gas. Why do these 
definitions mean more to you now than formerly? 

8. If a wire is stretched 0.3 cm. on applying 4 kg. of force, what 
force will stretch it 0.75 cm? Explain. 

9. How long will it take under ordinary conditions for a gas mole- 
cule to cross a room? Give reasons for your answer. 

10. What is meant by the elastic limit of a body? 

11. Without reaching the elastic limit, if a beam is depressed 4 mm. 
under a load of 60 kg., what will be the depression under a load 
of 400 kg.? Of 600 kg.? 

12. Name three substances that possess elasticity of volume. 

13. Give three examples of each; elasticity of (1) compression, (2) 
stretching, (3) torsion, (4) flexure 

Review Outline: Introduction and Molecules 

Physics; definition, topics considered, physical and chemical 

changes. 
Science; hypothesis, theory, law. Knowledge; common, scientific. 
Matter; three states, molecular theory. Mass, weight, volume. 
Metric system; units, tables, equivalents, advantages. 
Evidences of molecular motions; gases (3), liquids (5), solids (3). 
Evidences of molecular forces; liquids (3), solids (many) special 

properties such as: elasticity, tenacity, ductility, hardness, etc. 
Hooke's law; applications. 



CHAPTER III 



MECHANICS OF LIQUIDS 

(i) The Gravity Pressure of Liquids 

35. Pressure of Liquids against Surfaces. The sight 
of a great ship, perhaps built of iron and floating on 
water, causes one to wonder at the force that supports 
it. This same force is noticed when one pushes a light 
body, as a cork, under water. It is quite evident in 

such a case that a force exists 
sufficient to overcome the 
weight of the cork so that it 
tends to rise to the surface. 
Even the weight of our bodies 
is so far supported by water 
that many persons can float. 

The following experiment 
provides a means of testing 
this force: 



Fig. 17. Water forces the card 
against the chimney. 



If an empty can is pushed down into water, we feel at once the 
force of the liquid acting against the object and tending to push 
it upward. It may be noticed also that so long as the can is not 
completely submerged the deeper the can is pushed into the water 
the greater is the upward force exerted by the liquid. 

We may test this action in various ways: a simple way is to take 
a cylindrical lamp chimney, press a card against its lower end and 
place it in the water in a vertical position. The force of the water 
will hold the card firmly against the end of the chimney. (See Fig. 
17.) The amount of force may be tested by dropping shot into the 
tube until the card drops off. At greater depths more shot will be 
required, showing that the force of the water increases with the 
depth. Or one may pour water into the chimney. It will then be 

36 



MECHANICS OF LIQUIDS 37 

found that the card does not drop until the level of the water inside 
the chimney is the same as on the outside. That is, before the card 
will fall off, the water must stand as high within the chimney as 
without no matter to what depth the lower end of the chimney is 
thrust below the surface of the water. 

36. Law of Liquid Pressure. As there is twice as 
much water or shot in the chimney when it is filled to a 
depth of 10 cm. as there is when it is filled to a depth of 
5 cm. the force of the water upward on the bottom must 
be twice as great at a depth of 10 cm. as at a depth of 
5 cm. Since this reasoning will hold good for a comparison 
of forces at any two depths, we have the law: " The pres- 
sure exerted by a liquid is directly proportional to the depth." 

The amount of this force may be computed as follows : 
First, the card stays on the end of the tube until the 
weight of water from above equals the force of the water 
from below, and second, the card remains until the water is 
at the same height inside the tube as it is outside. Now 
if we find the weight of water at a given depth in the tube, 
we can determine the force of the water from below. If 
for instance the chimney has an area of cross-section of 
12 sq. cm. and is filled with water to a depth of 10 cm., 
the volume of the water contained will be 120 ccm. This 
volume of water will weigh 120 g. This represents then, 
not only the weight of the water in the tube, but also the 
force of the water against the bottom. In a similar way 
one may measure the force of water against any horizontal 
surface. 

37. Force and Pressure. We should now distinguish 
between force and pressure. Pressure refers to the force 
acting against unit area, while force refers to the action 
against the whole surface. Thus for example, the atmos- 
pheric pressure is often given as 15 pounds to the square 
inch or as one kilogram to the square centimeter. On 



38 PHYSICS 

the other hand, the air may exert a force of more than 300 
pounds upon each side of the hand of a man ; , or a large 
ship may be supported by the force of thousands of tons 
exerted by water against the bottom of the ship. 

In the illustration, given in Art. 36, the upward force 
of the water against the end of the tube at a depth of 10 
cm. is computed as 120 grams. The pressure at the same 
depth will be 10 grams per sq. cm. What will be the pres- 
sure at a depth of 20 cm.? at a depth of 50 cm.? of 100 
cm.? Compare these answers with the law of liquid pres- 
sure in Art. 36. 

38. Density. If other liquids, as alcohol, mercury, etc., 
were in the jar, the chimney would need filling to the 
same level outside, with the same liquid, before the card 
would fall off. This brings in a factor that was not con- 
sidered before, that of the mass* of a cubic centimeter of 
the liquid. This is called the density of the liquid. Alcohol 
has a density of 0.8 g. per cubic centimeter, mercury of 
13.6 g. per cubic centimeter, while water has a density of 
1 g. per cubic centimeter. 

39. Liquid Force against Any Surface. To rind the 
force exerted by a liquid against a surface we must take 
into consideration the area of the surface, and the height 
and the density of the liquid above the surface. The fol- 
lowing law, and the formula representing it, which con- 
cisely expresses the principle by which the force exerted 
by a liquid against any surface may be computed, should 
be memorized: 

The force which a liquid exerts against any surface, equals 
the area of the surface, times its average depth below the surface 
of the liquid, times the weight of unit volume of the liquid. 

Or, expressed by a formula, F = Ahd. In this formula, 
"F" stands for the force which a liquid exerts against any 

* The mass of a body is the amount cf matter in it, the weight is the 
pull of the earth upon it. 



MECHANICS OF LIQUIDS 39 

surface, "A" the area of the surface, "H, " for the average 
depth {or height) of the liquid pressing on the surface, and 
d", for the weight of unit volume of the liquid. This is 
the first illustration in this text, of the use of a formula to 
represent a law. Observe how accurately and concisely 
the law is expressed by the formula. When the formula 
is employed, however, we should keep in mind the law 
expressed by it. 

We must remember that a liquid presses not only down- 
ward and upward but sideways as well, as we see when 
water spurts out of a hole in the side of a vessel. Experi- 
ments have shown that at a point the pressure in a fluid 
is the same in all directions, hence the rule given above 
may be applied to the pressure of a liquid against the 
side of a tank, or boat, or other object, provided we are 
accurate in determining the average depth of the liquid; 
The following example illustrates the use of the law. 

For Example: If the English system is used, the area of the sur- 
face should be expressed in square feet, the depth in feet and the 
weight of the liquid in pounds per cubic foot. One cubic foot of 
water weighs 62.4 lbs. 

Suppose that a box 3 ft. square and 4 ft. deep is full of water. 
What force will be exerted by the water against the bottom and a 
side? 

From the law given above, the force of a liquid against a surface 
equals the product of the area of the surface, the depth of the liquid 
and its weight per unit volume, or using the formula, F = Ahd. 
To compute the downward force against the bottom we have the 
area, 9, depth, 4, and the weight 62.4 lbs. per cubic foot. oX 
4X62.4 lbs. = 2246.4 lbs. To compute the force against a side, the 
area is 12, the average depth of water on the side is 2, the weight 
62.4, 12X2X62.4 lbs. =1497.6 lbs. 

Important Topics 

1. Liquids exert pressure; the greater the depth the greater the 
pressure. 



40 PHYSICS 

2. Difference between force and pressure. 

3. Rules for finding upward and horizontal force exerted by a 
liquid. F = AM. 

4. Weight, mass, density. 

Exercises 

1. What is the density of water? 

2. What force is pressing upward against the bottom of a flat boat, 
if it is 60 ft. long, 15 ft. wide and sinks to a depth of 2 ft. in the 
water? What is the weight of the boat? 

3. If a loaded ship sinks in the water to an average depth of 20 ft., 
the area of the bottom being 6000 sq. ft., what is the upward 
force of the water? What is the weight of the ship? 

4. If this ship sinks only 10 ft. when empty, what is the weight of 
the ship alone? What was the weight of the cargo in Problem 

3? 

5. What is the liquid force against one side of an aquarium 10 ft. 
long, 4 ft. deep and full of water? 

6. What is the liquid force on one side of a liter cube full of water? 
Full of alcohol? Full of mercury? What force is pressing on 
the bottom in each case? 

7. What depth of water will produce a pressure of 1 g. per square 
centimeter? 10 g. per square centimeter? 1000 g. per square 
centimeter? 

8. What depth of water will produce a pressure of 1 lb. per square 
inch? 10 lbs. per square inch? 100 lbs. per square inch? 

9. What will be the force against a vertical dam-breast 30 meters 
long, the depth of the water being 10 meters? 

10. A trap door with an area of 100 sq. dcm. is set in the bottom 
of a tank containing water 5 meters deep. What force does 
the water exert against the trap door? 

11. What is the force on the bottom of a conical tank, filled with 
water, the bottom of which is 3 meters in diameter, the depth 
1.5 meters? 

12. If alcohol, density 0.8 were used in problem n, what would be 
the force? What would be the depth of alcohol to have the 
same force on the bottom as in problem n? 

13. What is the pressure in pounds per square inch at a depth of 
1 mile in sea water, density 1.026 grams per cc? 



MECHANICS OF LIQUIDS 



41 



14. Find the force on the sides and bottom of a rectangular cis- 
tern filled with water, 20 ft. long, 10 ft. wide, and 10 ft. deep? 

15. Find the force on the bottom of a water tank 14 ft. in diameter 
when the water is 1 5 ft. deep, when full of water. 

16. Find the force on one side of a cistern 8 ft. deep and 10 ft. 
square, when full of water. 

17. Find the force on a vertical dam 300 ft. long and 10 ft. high, 
when full of water. 

18. Find the pressure at the bottom of the dam in question 17. 

19. Why are dams made thicker at the bottom than at the top? 

20. A ship draws 26 ft. of water, i.e., its keel is 26 ft. under water. 
What is the liquid force against a square foot surface of the 
keel? Find the pressure on the bottom. 



(2) Transmission .of Liquid Pressure 

40. Pascal's Principle. Liquids exert pressure not only 
due to their own weight, but when confined, may be made 
to transmit pressure to considerable distances. This is a 
matter of common knowledge wherever a system of water- 
works with connections to houses is found, as in cities. 
The transmission of liquid pressure 
has a number of important applica- 
tions. The principle underlying each 
of these was first discovered by Pascal, 
a French scientis'" of the seventeenth 
century. Pascal's Principle, as it is 
called, may be illustrated as follows: 

Suppose a vessel of the shape shown in Fig. 
18, the upper part of which we may assume 
has an area of 1 sq. cm., is filled with water 
up to the level AB. A pressure will be 
exerted upon each square centimeter of area 
depending upon the depth. Suppose that the 
height of AB above CD is 10 cm., then the force upon 1 sq. cm. 
of CD is 10 g., or if the area of CD is 16 sq. cm., it receives a force 
of 160 g. 




Fig. 18. 
increases 
depth. 



-The force 
with the 



42 



PHYSICS 



If now a cubic centimeter of water be poured upon A Bit will raise 
the level i cm., or the head of water exerting pressure upon CD be- 
comes ii cm., or the total force in CD is 16X11 g., ie., each square 
centimeter of CD receives an additional force of 1 g. Hence the 
force exerted on a unit area at AB is transmitted to every unit area 
within the vessel. 

The usual form in which this law is expressed is as 
follows: Pressure applied to any part of a confined liquid 
is transmitted unchanged, in all directions, and adds the same 
force to all equal surfaces in contact with the liquid. 




Fig. 19. The force is proportional to the area. 



The importance of this principle, as Pascal himself 
pointed out, lies in the fact that by its aid we are able to 
exert a great force upon a large area by applying a small 
force upon a small area of a confined liquid, both areas 
being in contact with the same liquid. Thus in Fig. 19 
if the area of the surface CD is 2000 times the area of the 
surface AB, then 1 lb. applied to the liquid on AB will 
exert or sustain a force of 2000 lbs. on CD. 

41. Hydraulic Press. An important application of 
Pascal's principle is the hydraulic press. See Fig. 20. 
It is used for many purposes where greatforce is required, 
as in pressing paper or cloth, extracting oil from seeds, 
lifting heavy objects, etc. Many high school pupils 
have been seated in a hydraulic chair used by a dentist or 
barber. This chair is a modified hydraulic press. 



MECHANICS OF LIQUIDS 



43 



The hydraulic press contains two movable pistons, P 
and p (see Fig. 20). The larger of these, P, has a cross- 
sectional area that may be 100 or 1000 times that of the 
smaller. The smaller one is moved up and down by a 
lever; on each upstroke, liquid is drawn in from a reservoir, 
while each down-stroke forces some of the liquid into the 
space about the large piston. Valves at V and V prevent 
the return of the liquid. If the area -of P is 1,000 times 




Fig. 20. Cross-section of a hydraulic press. 



that of p, then the force exerted by P is 1000 times the 
force employed in moving p. On the other hand, since 
the liquid moved by the small piston is distributed over 
the area of the large one, the latter will move only Mo 00 
as far as does the small piston. The relation between the 
motions of the two pistons and the forces exerted by them 
may be stated concisely as follows: The motions of the 
two pistons of the hydraulic press are inversely propor- 
tional to the forces exerted by them. The cross-sectional 
areas of the two pistons are, on the other hand, directly 
proportional to the forces exerted by them. 

An application of Pascal's principle often employed in 



44 



PHYSICS 



cities is the hydraulic elevator. In this device a long 
plunger- or piston extends downward from the elevator car 

into a cylinder sunk into the 
earth, sometimes to a depth 
of 300 ft. Water forced 
into this cylinder pushes 
the piston upward and 
when the water is released 
from the cylinder the piston 
descends. 

Fig. 21 represents another form 
of hydraulic elevator, where the 
cylinder and piston are at one 
side of the elevator shaft. In 
this type, to raise the elevator, 
water is admitted to the cylinder 
pushing the piston downward. 

42. Artesian Wells. 

Sometimes a porous stratum 
containing water in the 
earth's crust is inclined. 
Then if there are impervious 
strata (see Fig. 22), both 
above and below the water- 
bearing one, and the latter 
comes to the surface so that 
rain may fill it, a well sunk 
to the water-bearing stratum 
at a point where it is below 
the surface will usually give 
an artesian well, that is, one 

in which the water rises to or above the surface. Many 

are found in the United States'. 
43. Standpipes and Air Cushions. 




Fig. 21.- 



-A hydraulic freight ele- 
vator. 



-Many who have 



MECHANICS OF LIQUIDS 



45 



lived in cities where water is pumped into houses under 
pressure know that the water pressure is changed when 



Fig. 22. Conditions producing an artesian well. 

several faucets are opened at the same time. Again, if 
several persons are using a hose for sprinkling, the pressure 



* 



Fig. 23. A standpipe. 

may be lessened so as to be insufficient to force the water 
above the first floor. In order to allow for these changes 
some flexibility or spring must be introduced somewhere 



46 PHYSICS 

intjp the water-pipe system. Water is nearly incompressi- 
ble and if no means were employed to take care of the 
pressure changes, the sudden stopping and starting of 
the flow would cause serious jars and start leaks in the 
pipes. Two common devices for controlling sudden 
changes in the water pressure are the standpipe and the 
air cushion. 

The standpipe is simply a large vertical tube connected to the 
water mains from which and into which water readily flows. When 
many faucets are opened the water lowers; when most faucets are 
closed the water rises, giving a simple automatic control of the 
surplus water and a supply of water for a short time during a shut- 
down of the pumps. Standpipes are often used in towns and small 
cities. Fig. 23 represents the standpipe at Jerome, Idaho. 

The air cushion (Fig. 24) is a 
metal pipe or dome filled with air 
attached to a water pipe where sud- 
den changes in pressure are to be 
controlled. At many faucets in a 
city water system such an air 
cushion is employed. It contains 
air; this, unlike water, is easily com- 
pressible and the confined air when 

_ .-.. the tap is suddenly closed receives 

Fig. 24. The short pipe , , , , , , , 

above the faucet contains air and checks gradually the rush of 

forming an air cushion. water in the pipe. Even with an air 

cushion, the "pound" of the water 
in the pipe when a tap is suddenly closed is often heard. If air 
cushions were not provided, the "water hammer" would frequently 
crack or break the pipes. 

Important Topics 

1. Pascal's law. 

2. Hydraulic press. 

3. Artesian wells. 

4. Standpipes and air cushions. 




MECHANICS OF LIQUIDS 47 

Exercises 

i. Where have you seen an air cushion? Describe it and its use. 

2. Where have you seen an hydraulic press? Why and how used? 

3. Where have you seen hydraulic elevators? What moves them? 

4. Where do you know of liquids under pressure? Three examples. 

5. What is the pressure in water at a depth of 1 500 cm. Express 
in grams per square centimeter and in kilograms per square 
centimeter. 

6. What head 1 of water is required to give a pressure of 200 g. per 
1 "Head" is a term used to express the vertical height of water in pipes. 

square centimeter? 2 kg. per square centimeter? 

7. What pressure will be produced by a "head" of water of 20 
meters? 

8. If 1728 en. in. of water are placed in a vertical tubei sq. in. 
in cross section to what height would the water rise? It would 
give how many feet of head? 

9. What would the water in problem 8 weigh? What pressure 
would it produce at the bottom, in pounds per square inch? 
From this, compute how many feet of "head" of water will 
produce a pressure of 1 lb. per square inch. 

10. Using the result in problem 9, what "head" of water will pro- 
duce a pressure of 10 lbs. per square inch? 100 lbs. per square 
inch? 

11. From the result in 9, 100 ft. of "head" of water will produce 
what pressure? 1000 ft. of "head?" 

12. If the diameter of the pump piston in a hydraulic press in 2 cm. 
and that of the press piston 50 cm. what will be the force 
against the latter if the former is pushed down with a force of 
40 kg.? 

(3) Archimedes' Principle 

44. A Body Supported by a Liquid. Among the 
applications of the force exerted by a liquid upon a surface, 
Archimedes' Principle is one of the most important. 

Most persons have noted that a body placed in water is 
partly or wholly supported by the force of the water upon 
it. A stone held by a cord and lowered into water is felt 



48 



PHYSICS 



to have a part of its weight supported, while a piece of 
cork or wood is wholly supported and floats. 

The human body is almost entirely supported in water, 
in fact, many people can easily float in water. It was the 
consideration of this fact that led the Greek philosopher 
Archimedes to discover and state the principle that de- 
scribes the supporting of a body in a liquid. 

45. Archimedes' Principle. "A body immersed in a 
liquid is pushed up by a force equal to the weight of the 

liquid that it displaces." The proof 
for this law is simply demonstrated. 
Suppose a cube, abed, is immersed in 
water (Fig. 25). The upward force 
on cd is equal to the. weight of a 
column of water equal to cdef. (See 
Art. 39.) The downward force 
upon the top of the cube is equal 
to the weight of the column of water 
abef. Then the net upward force 
upon the cube, that is, the upward 
force upon the bottom less the down- 
ward force upon the top, or the 

buoyant force exerted by the liquid is exactly equal to 

the weight of the displaced water abed. 

46. Law of Floating Bodies. This same reasoning 
may be applied to any liquid and to any body immersed 
to any depth below the surface of the liquid. If the body 
weighs more than the displaced liquid it will sink. If it 
weighs less than the displaced liquid it will float or rise 
in the water. A block of wood rises out of the water in 
which it floats until its own weight just equals the weight 
of the water it displaces. From this we have the law of 
floating bodies. 




Fig. 25. Theoretical 
proof of Archimedes' 
principle. 



'MECHANICS OF LIQUIDS 



49 






A floating body displaces its own weight of the liquid in 
which it floats. 

To test the law of floating bodies, take a rod of light 
wood i cm. square and 30 cm. long (Fig. 
26). Bore out one end and fill the opening 
with lead and seal with paraffin so that the 
rod will float vertically when placed in water. 
Mark upon one side of the rod a centimeter 
scale, and dip the rod in hot paraffin to 
make it waterproof. Now find the weight 
of the stick in grams and note the depth to 
which it sinks in water in centimeters. 
Compute the weight of the displaced water. 
It will equal the weight of the rod. 

47. Applications of Archimedes' Principle. 
There are numerous applications of Arch- 
imedes' Principle and the law of floating bodies. 



Fig. 26. A 
floating body 
displaces its 
own weight of 
water. 



(a) To Find the Weight of a Floating Body : Problem. A boat 
20 ft. long and with an average width of 6 ft. sinks to an average 
depth of 3 ft. in the water. Find the weight of the boat. What 
weight of cargo will sink it to an average depth of 5 ft.? 

Solution. The volume of the water displaced is 20 X 6 X 3 cu. 
ft. = 360 cu. ft. Since 1 cu. ft. of water weighs 62.4 lbs., 360 X 
62.4 lbs. = 22,464 lbs., the weight of water displaced. By the law of 
floating bodies this is equal to the weight of the boat. When loaded 
the volume of water displaced is 20 ft. X 6 X 5 ft. which equal 600 
cu. ft. 600 X 62.4 lbs. = 37,440 lbs. This is the weight of the water 
displaced when loaded. 37,440 lbs. 22,464 lbs. = 14,976 lbs., the 
weight of the cargo. 

(b) To Find the Volume of an Immersed Solid : Problem. A 
stone weighs 187.2 lbs. in air and appears to weigh 124.8 lbs. in 
water. What is its volume? 

Solution. 187.2 lbs. 124.8 lbs. = 62.4 lbs., the buoyant force of 
the water. By Archimedes' Principle, this equals the weight of the 
displaced water which has a volume of 1 cu. ft. which is therefore the 
volume of the stone. 
4 



So 



PHYSICS 



(c) To Find the Density of a Body : The density of a body is 
defined as the mass of unit volume. 

We can easily find the mass of a body by weighing it, but the 
volume is often impossible to obtain by measurements, especially 
of irregular solids. 

Archimedes' Principle, how- 
ever, provides a method of 
finding the volume of a body 
accurately by weighing it first 
in air and then in water (Fig. 
27), the apparent loss in weight 
being equal to the weight of the 
displaced"" water. One needs 
only to find the volume of 
water having the same weight 
as the loss of weight to find 
the volume of the body. 

If the metric system is used, 
1 ccm. of water weighs 1 g., 

and the volume is numerically the same as the loss of 

weight. 



Fig. 27. A method of weighing 
a body under water. 



Important Topics 

1. Archimedes' Principle. 

2. Law of floating bodies. 

3. The applications of Archimedes' Principle are to determine (a) 
the weight of a floating body; (b) the volume of an immersed 
solid, and (c) the density of a body. 

Exercises 



1. Look up the story of Archimedes and the crown. Write a 

brief account of it. 
2. Why is it easier for a fat man to float in water than for a lean 
one? 



MECHANICS OF LIQUIDS 5 1 

3. A fish weighing 1 lb. is placed in a pail full of water. Will the 
pail and contents weigh more than before adding the fish? 
Why? 

4. Why can a large stone be lifted more easily while under water 
than when on the land? 

5. Why does the air bubble in a spirit level move as one end of the 
instrument is raised or lowered? 

6. Why does a dead fish always float? 

7. A ship is built for use in fresh water. What will be the effect 
on its water line when passing into the ocean? 

8. Why can small bugs walk on water while large animals cannot ? 

9. If an object weighing 62.4 lbs. just floats in water, what weight 
of water does it displace? What volume of water is displaced? 
What is the volume of the body? 

10. What is the volume of a man who just floats in water if he 
weighs 124.8 lbs.? If he weighs 187.2 lbs.? 

11. An object weighing 500 g. just floats in water. What is its 
volume? How much water does a floating block of wood 
displace if it weighs 125 lbs.? 125 g.? 2 kg.? 2000 kg.? 

12. A flat boat 10 X 40 ft. in size will sink how much in the 
water when 10 horses each weighing 1250 lbs. are placed on 
board? 

13. A ship 900 ft. long and 80 ft. average width sinks to an average 
depth of 25 ft. when empty and 40 ft. when loaded. What is 
the weight of the ship and of its load? 

14. Will a 1000 cc. block sink or float in water if it weighs 800 g.? 
If it weighs 1200 g.? Explain. 

15. If a 1000 cc. block of metal weighing 1200 g. is placed in the 
water in mid ocean what will become of it? 

16. Prove Archimedes' Principle by use of the principles of liquid 
pressure. 

17. An irregular stone, density 2.5, g. per ccm. displaces 2 cu. ft. of 
water What is its weight ? Its apparent weight in water? 

18. Will the depth to which a vessel sinks in water change as she 
sails from Lake Ontario into the Atlantic Ocean? Why? 

19. If the density of sea water is 1.0269 g- per cubic centimeter and 
that of ice 0.918 g. per ccm., what portion of an iceberg is above 
water? 

20. In drawing water from a well by means of a bucket, why is 
less force used when it is under water than when entirely above? 



52 PHYSICS 

21. A stone which weighs 300 lbs. can be lifted under water with a 
force of 150 lbs. What is the volume of the stone? 

22. The average density of the human body is 1.07 grams per c.c. 
How much water will a man who weighs 150 lbs. displace when 
diving? How much when floating? 

(4) Density and Specific Gravity 

48. Density. The density of a substance is often used 
as a test of its purity. Archimedes in testing King Hiero's 
crown to find out if it were made of pure gold, determined 
first its density. It is by such tests that the purity of 
milk, of alcohol, of gold, and a great variety of sub- 
stances is often determined. 

Knowledge of methods of finding density is of value to 
everyone and should be included in the education of every 
student. The density of a substance is the mass of unit 
volume of the substance. In the metric system, for example, 
the density of a substance is the mass in grams per 1 ccm. 
Taking water, 1 ccm. weighs 1 gr. or its density is there- 
fore 1 g. to the cubic centimeter. A cubic centimeter 
of aluminium weighs 2.7 g. Its density therefore is 2.7 g. 
per ccm. 

49. Specific Gravity. Specific gravity is the ratio of the 
weight of any volvme of a substance to the weight of an 
equal volume of water. Its meaning is not quite the same 
as that of density, since specific gravity is always a ratio, 
i.e., an abstract number, as 2.7. Density of a substance 
is a concrete number, as 2.7 grams per ccm. In the 
metric system the density of water is one gram per cubic 
centimeter, therefore we have: 

Density (g. per ccm.) = (numerically) specific gravity. 
In the English system, the density of water is 62.4 
pounds per cubic foot, therefore in this system we have: 
Density (lbs. per cu. ft.) = (numerically) 62.4 X sp. gr. 



MECHANICS OF LIQUIDS 53 

50. Methods for Finding Density and Specific Gravity 
(a) Regular Solids. Solids of regular shapes such as cubes, 
spheres, etc., whose volumes may be readily found by 
measurement, may be weighed. The mass divided by the 
volume gives the density, or D = Mn/v. 

(b) Irregular Solids. With these the volume cannot be 
found by measurement but may be obtained by Archi- 
medes' Principle. Weigh the solid first in the air and 
then in water. The apparent loss of weight equals the 
weight of the equal volume of water displaced. From 
this the volume may be found. And then the 

mass , . r 

density equals j ; the specific gravity = 

wt. in air wt. in air 

wt. of equal volume of water (wt. in air) (wt. in water) 

(c) Solids Lighter than Water. This will require a 
sinker to hold the body under water. Weigh the solid 
in air (w). Weigh the sinker in water (s). Attach 
the sinker to the solid and weigh both in water (w f ). 
The specific gravity equals 

wt. of solid in air w 



or 



loss in wt. of solid in water (w + s) w' 

The apparent loss of weight of the solid is equal to the sum 
of its weight in air plus the weight of the sinker in water, 
less the combined weight of both in water. 

(d) The Density of a Liquid by a Hydrometer. One 
may also easily find the density of any liquid by Archi- 
medes' Principle. If one takes the rod described in Art. 
46, and places it in water, the number of cubic centimeters 
of water it displaces indicates its weight in grams. On 
placing the rod in another liquid in which it floats, it will 
of course displace its own weight and the height to which 
the liquid rises on the scale gives the volume. By divid- 



54 



PHYSICS 



ing the weight of the rod as shown by its position in water 
by the volume of the liquid displaced we obtain the density 
of the liquid. Commercial hydrometers 
for testing the density of milk, alcohol 
and other liquids are made of glass of the 
form shown in Fig. 28. The long narrow 
stem permits small differences in volume 
to be noticed, hence they are more 
accurate than the rod described in the 
preceding paragraph. For convenience 
this rod contains a paper scale, so that 
when the height of the liquid on the stem 
is noted, the density is read at once. 

Density of Liquids by Loss of Weight. 
Weigh a piece of glass in air (W a ), in 
water (W w ), and in the liquid to be 
tested (Wi). 

Then (W a W w ) gives the weight of the water displaced 
And (W a W\) gives the weight of the liquid displaced 



Fig. 28. A hy- 
drometer used to 
find the density 
of a liquid. 



Hence, 



W a -Wl 



equals the specific gravity of the liquid. 



W a -Wn 

Important Topics 

Definitions of density and specific gravity. 

Methods of finding density: (a) regular solids; (b) irregular 
solids; (c) solids lighter than water; (d) liquids by hydromter; 
(e) liquids by loss of weight. 



Exercises 



Con- 



Note. Consider that 1 cu. ft. of water weighs 62.4 lbs. 
sider that 1 ccm. of water weighs 1 g. 
1. What is meant by the statement that a block of wood has a 
specific gravity of 0.6? 

2. Considering that the density of the human body is the same as 
that of water, what is the volume of a 125-lb. boy? Of a 250-lb. 
man? Of a 62.4-lb. boy? What is the volume of your body? 

3. How is the weight of large ships found? Give an example. 



MECHANICS OF LIQUIDS 55 

4. Mention three cases where determinations of density are im- 
portant. 

5. A body weighs 40 g. in air, 15 g. in water, 5 g. in an acid. Find 
(a) the density of the body; (b) its volume; (c) density of the 
acid. 

6. If the specific gravity of a horse is 1, what is the volume of a 
horse weighing 500 kg.? Of one weighing 1248 lbs.? 

7. A weighted wooden box sinks to a depth of 20 cm. in water and 
24 cm. in alcohol, and to a depth of 18 cm. in brine. What is 
the density of the alcohol and of the brine? 

8. A glass stopper weighs in the air 25 g., in water 15 g., in oil 18 g. 
Find the density and volume of the stopper. Find the density 
of the oil. 

19. What would a cubic foot of wood weigh if the specific gravity 
were 0.5.? 

10. The specific gravity of aluminum is 2.7. Find the weight of 
a cubic foot of it. 

11. A block of wood weighs 40 g. A piece of lead appears to weigh 
70 g. in water. Both together appear to weigh 60 g. in water. 
Find the density of the wood. 

12. A stone weighs 30 g. in air, 22 g. in water, and 20 g. in salt 
water. Find the density of the salt water. 

13. Will iron sink in mercury? Why? 

14. A submarine boat weighing 200 tons must have what volume 
in order to float? 

15. Find the weight of 2 cu. ft. of copper from its density. 

16. What is the weight in water of a mass whose specific gravity is 
3.3 and whose weight is 50 kg.? 

17. A block of granite weighs 1656 lbs.; its volume is* 10 cu. ft., 
what is its density? 

18. If the specific gravity of hard coal is 1.75 how would you 
determine how many tons of coal a bin would hold? 

19. A hollow copper ball weighs 2 kg. What must be its volume to 
enable it to just float in water? 

20. A mass having a volume of 100 ccm. and a specific gravity 
of 2.67 is fastened to 200 ccm. of wood, specific gravity 0.55. 
What will the combination weigh in water? 

21. A block weighing 4 oz. in air is tied to a sinker which appears to 
weigh 14 oz. in water. Both together appear to weigh 6 oz. 
in water. What is the specific gravity of the block? 



CHAPTER IV 



MECHANICS OF GASES 



(i) Weight and Pressure of the Air 

51. Weight of Air. It is said that savages are unaware 
of the presence of air. They feel the wind and hear and 
see it moving the leaves and branches of the trees, but of 
air itself they have little conception. 

To ordinary observers, it seems to have no weight, and 
to offer little resistance to bodies passing- through it. 
That it has weight may be readily shown as follows: 

(See Fig. 29.) If a hollow metal 
sphere, or a glass flask, provided 
with tube and stopcock, be 
weighed when the stopcock is 
open, and then after the air has 
been exhausted from it by an air 
pump, a definite loss of weight is 
noticeable. 

If the volume of the sphere is 
known and it is well exhausted 
of air, a fair approximation of 
the weight of air may be obtained. Under "standard 
conditions," which means at the freezing temperature and 
a barometric pressure of 76 cm., a liter of air weighs 
1.293 g- while 12 cu. ft. of air weigh approximately 1 lb. 

52. Pressure of Air. Since air has weight it may 
be supposed to exert pressure like a liquid. That it 
does so may be shown in a variety of ways. 

56 




Fig. 29. 



-Proof that air has 
weight. 



MECHANICS OF GASES 



57 





\ 
111 



If a plunger fitting tightly in a glass cylinder be drawn 
upward, while the lower end of the tube is under water, 
the water will rise in the tube (Fig. 30). The common 
explanation of this is that the water rises because of 
"suction." The philosophers of the ancient Greeks ex- 
plained it by saying that "nature abhors 
a vacuum," and therefore the water rises. 
Neither explanation is correct. It was 
found in 1640 that water would not rise 
in a pump more than 32 ft. despite the fact 
that a vacuum was maintained above the 
water Galileo was applied to for an 
explanation. He said, " evidently nature's 
horror of a vacuum does not extend above 
32 ft." Galileo began tests upon "the 
power of a vacuum" but dying left his 
pupil Torricelli to continue the experi- 
ment, rorricelli reasoned that if water 
would rise 32 ft., then mercury, which is 
13.6 times as dense as water, would rise 
about 3^3 as much. To test this, he performed the follow- 
ing famous experiment. 

53. Torricelli's Experiment (1643). Take a glass tube 
about 3 ft. long, sealed at one end, and fill it with mercury. 
Close the end with the finger and invert, placing the end 
closed by the finger under mercury in a dish (Fig. 31). 
Remove the finger and the mercury sinks until the top 
of the mercury is about 30 in. above the level of the mer- 
cury in the dish. Torricelli concluded that the rise of 
liquids in exhausted tubes is due to the pressure of the 
atmosphere acting on the surface of the mercury in the 
dish. 

To test this, place the tube with its mercury upon the 
plate of an air pump and place a tubulated bell jar over 



Fig. 30. Air 
pressure forces 
the liquid up the 
tube. 



58 



PHYSICS 



the apparatus so that the tube projects through a tightly 
fitting stopper. (See Fig. 32.) If the air pressure is the 
cause of the rise of mercury in the tube, on removing the 
air from the bell jar the mercury should fall in the tube. 
This is seen to happen as soon as the pump is started. It 
is difficult to remove all the air from the receiver so the 
mercury rarely falls to the same level in the tube as in 





Fig. 31. Torricelli's experiment. 



Fig. 32. The mercury drops 
as the air is removed. 



the dish. A small tube containing mercury is often at- 
tached to air pumps to indicate the degree of exhaustion. 
Such tubes are called manometers. 

54. The Amount of Atmospheric Pressure. Torri- 
celli's experiment enables us to compute readily the 
pressure of the atmosphere, since it is the atmospheric 
pressure that balances the column of mercury in the 
tube. By Pascal's Law, the pressure of the atmos- 
phere on the surface of the mercury in the dish is trans- 
mitted as an exactly equal pressure on the mercury 



MECHANICS OF GASES 



59 




column in the tube at the same level as the mercury 
outside. 

This pressure, due to the air, must bal- 
ance the weight of the column of mercury 
in the tube. It therefore equals the weight 
of the column of mercury of unit cross- 
section. The average height of the column 
of mercury at sea-level is 76 cm. Since the 
weight of 1 cc. of mercury is 13.6 grams, 
the pressure inside the tube at the level of 
the surface of the mercury in the dish is 
equal to 1 X 76 X 13.6 or 1033.6 g. per 
square centimeter. Therefore the atmos- 
pheric pressure on the surface of the mercury 
in the dish is 1033.6 g. per square centimeter, 
approximately 1 kg. per square centimeter or 
15 lbs. per square inch. 

55. Pascal's Experiment. Pascal tested 
in another way the action of atmospheric 
pressure upon the column of mercury by 
requesting his brother-in-law, Perrier, who 
lived near a mountain, to try the experiment 
on its top. Perrier found that on ascending 
1000 meters the mercury fell 8 cm. in the 
tube. Travelers, surveyors, and aviators 
frequently determine the altitude above 
sea-level by reading the barometer, an 
ascent of n meters giving a fall of about 
1 mm. in the mercury column, or 0.1 in. for 
every 90 ft. of ascent. 

56. The Barometer. The modern baro- 
meter (Fig. 33), consists of a Torricellian 

tube properly mounted. Reading a barometer consists 
in accurately reading the height of the mercury column. 




Fig. 33. A 
standard 
barometer. 



60 PHYSICS 

This height varies from 75 to 76.5 cm. or 29 to 30 in. 
in localities not far from the sea-level. The atmospheric 
pressure varies because of disturbances in the atmos- 
phere. It is found that these disturbances of the atmos- 
phere pass across the country from west to east in a 
somewhat regular manner, hence a series of readings of 
the barometer may give reliable information of the move- 



FiG. 34. An aneroid barometer 

ment of these disturbances and so assist in forecasting the 
weather. The Weather Bureau has observations taken 
at the same moment at various stations over the country. 
These observations form the basis for the daily forecast 
of the weather. 

Another form of barometer in common use is the Aneroid Baro- 
meter (Fig. 34). Its essential parts are a cylindrical air-tight box 
with an elastic corrugated cover. Inside the box is a partial vac- 
uum. This makes the cover very sensitive to slight changes of 
pressure. The motion of the top of the box is conveyed by a series 
of levers to an indicating hand which moves over a dial. This 



MECHANICS OF GASES 



61 



barometer can be made so sensitive as to indicate the change of 
air pressure from a table top to the floor. It is much used by- 
travelers, explorers, surveying parties and aviators, since the mer- 
curial barometer is inconvenient to carry. 



Important Topics 

1. Weight and Pressure of air in English and metric units, 
shown. Evidences. 

2. Work of Galileo, Torricelli, and Perrier. 

3. Barometer: construction, action, mercurial, aneroid. 



How 





Fig. 35. Air pressure keeps the 
water in the tumbler. 



Fig. 36. Cross-section of a 
modern drinking fountain. 



Exercises 



1. 



Do you think Archimedes' Principle applies to the air? Does 
Pascal' sLaw? Why? 

Find the downward pressure of the mercury in a barometer 
tube if the cross-section is 1 sq. cm. and the height 75 cm. at 
the level of the mercury surface in contact with the air. 
(The density of mercury is 13.6 grams per cc.) 



62 PHYSICS 

3. What is the weight of the air in a room if it is 10X8X4 meters? 

4. What weight of air is in a room 10X15X10 ft.? 

5. When smoke rises in a straight line from chimneys, is it an 
indication of a high or low barometric pressure? Why? 

6. Why does a tumbler filled with water and inverted in a dish 
with its rim under water remain full? 

7. If the barometer tube is inclined the mercury remains at the 
same horizontal level. How can this be explained? 

8. When the mercurial barometer stands at 76 cm., how high would 
7 a water barometer stand? Explain. 

9. Explain why it is possible for one to suck soda water through a 
tube? 

10. Fill a tumbler with water. Place a sheet of paper over the top 
and invert. The paper clings to the tumbler and prevents the 
water from escaping. Explain. (See Fig. 35.) 

11. Why must a kerosene oil can have two openings in order to 
allow the oil to flow freely? 

12. Explain the action of the modern drinking fountain (Fig. 36). 

(2) Compressibility and Expansibility of the air 

57. Effect of Prefssure on Liquids and Gases. Both 
classes of fluids, liquids and gases, have many character- 
istics in common. Both are composed of molecules that 
move freely; hence both flow. At any point within a fluid 
the pressure is the same in all directions. Archimedes' 
Principle applies, therefore, to both liquids and gases. 

We now come to an important difference between liquids 
and gases. Liquids are practically incompressible. "So 
much so, that if water is subjected to a pressure of 3000 
kg. per sq. cm., its volume is reduced only about one- 
tenth." Gases show a very different behavior from liquids 
on being subjected to pressure. They may readily be 
compressed to a small fraction of their volume as is noticed 
on inflating a pneumatic tire. A gas has also the ability to 
spring back to a larger volume as soon as the pressure is 
released, as when a cork is driven from a pop gun. Not 



MECHANICS OF GASES 



63 



only is compressed air able to expand, but air under ordi- 
nary conditions will expand if it is released in a space 
where the pressure is less. 

Hollow bodies, animals and plants, are not crushed by 
atmospheric pressure, because the air and gases con- 
tained within exert as much 
force outward as the air exerts 
inward. 

58. Boyle's Law. The re- 
lation between the volume and 
pressure of a gas was first in- 
vestigated by Robert Boyle in 
the seventeenth century. The 
experiment by which he first 
discovered the law or the re- 
lation between the volume and 
the pressure of a gas is briefly 

described as follows: 

JB 
A glass tube is bent in the form of 
the capital letter J, the short arm 
being closed. A little mercury is 
poured in to cover the bend. (See 
Fig. 370.) Since the mercury is at 
the same level in both arms, the pres- 
sure in (A) is the same as in (B). 
Mercury is now poured into (A) 
until it stands in the long tube at a height above that in (B) 
which is equal to the height of the mercury column of the barom- 
eter. (See Fig. 37ft.) The air in {BC) is now under a pressure of 
two atmospheres (one atmosphere is due to the mercury column). 
On measurement the air in (BC) will be found to have just one- 
half of its original volume. 



3 JS 

xr \g or 



Fig. 37 a. Fig. 37 6. 

Figs. 37 a and 37 b. Boyle's 
law apparatus. 



Thus doubling the pressure to which a gas is subjected 
reduces its volume to one-half. Tripling the pressure, re- 
duces the volume to one-third and so on. 



6 4 



PHYSICS 



Careful experiments reveal the following law: The 
volume of a given mass o] gas at constant temperature is 
inversely proportional to the pressure to which it is subjected. 

P V 



<= -=r, or 



This law is often expressed mathematically. , 

PV = P'V. Since doubling the pressure reduces the 



Tripling the 
P D 



volume one-half, it doubles the density 

pressure triples the density 

or the density of a gas directly proportional to its pressure 



We therefore have p> = ^, 



Heights 
in miles 



Barometer 
heights in 
inches 



35- 



IS- 



10-- 



0- 




\-is 



-JO 



Air 
densities 



Fig. 38. Height and density of the air. 



59. Height of the Atmosphere. From its properties 
of compression and expansion, the air varies in density 
and pressure as one ascends in it. At a height of 3 miles 
the pressure is reduced to about one-half. This is an 
indication that one-half of the air is below this level. 
Balloonists have gone to a height of 7 miles, Glaser and 



MECHANICS OF GASES 65 

Coxwell in England in 1862 and Berson in France in 1901. 
The atmosphere has been explored to a height of 30,500 
meters (18.95 miles) by sending up self -registering barom- 
eters in small balloons which burst at great altitudes. 
A parachute protects the instruments from breakage 
from too rapid fall. This height of 30,500 meters was 
reached by a balloon sent up by William R. Blair, at 
Huron, South Dakota, September 1, 1910. 

At a height of 35 miles, the density is estimated at 
1/30,000 of its value at sea-level. (See Fig. 38.) It is 
believed that some rarefied air exists for a considerable 
distance above this point, some estimates placing the ex- 
tent at 100 miles, and others from 200 to 500 miles. Evi- 
dences of some air at such heights are shown by: (a) 
the height at which meteors first appear, (b) the height of 
the Aurora Borealis, and (c), the distance that the sun 
is below the horizon when the last traces of color disappear 
from the sky in the evening. 

Although the exact limits of the atmosphere are un- 
known, the weight of a column of air 1 sq. cm. in cross- 
section, and extending upward as high as the atmosphere, 
may be accurately computed. For this column of air 
exactly balances the column of mercury in the tube of 
the barometer. 

Below sea-level, the air increases rapidly in density and 
it is estimated that at a depth of 35 miles, the density of 
the air would be a thousand times that at the earth's 
surface, or more than that of water. 

Important Topics 

1. Evidence of compressibility of gases and incompressibility of 
liquids. 

2. Boyle's Law. Proof, applications. 

3. Extent of the atmosphere three evidences. 

5 



66 



PHYSICS 



2. 



Exercises 

Mention three illustrations of the compressibility and ex- 
pansibility of air that you know from you own experience. 
Increasing the pressure increases the amount of a gas that will 
be absorbed by a liquid? Explain this. Have you ever ob- 
served this fact? Where? 

If a toy balloon containing 2000 ccm. of gas at the earth's surface 
where the barometer reading is 76 cm., rises to an elevation where 
the barometer reads 54 cm., the balloon will tend to expand to 
what volume? Explain. Will it attain this volume? 
If a gas is compressed, it changes in temperature. How do 
you explain this? 

What change in temperature will occur when compressed air 
is allowed to expand? Explain. 

Air blowing up a mountain side has its pressure lessened as 
it approaches the top. How will this affect the temperature? 
Why? What may result from this change in temperature? 
Explain. 

To what pressure must 500 ccm. of air be subjected to compress 
it to 300 ccm. the barometer reading at first being 75 cm. 
Explain. 




Fig. 39. The air pump. 

(3) Pneumatic Appliances 

60. The Air Pump. The air pump is used to remove air 
or other gases from a closed vessel. It was invented 
about 1650 by Otto Von Guericke, burgomaster of Magde- 



MECHANICS OF GASES 



6 7 



burg, Germany. One form of air pump is shown in Fig. 
39. C is a cylinder within which slides a tightly fitting 
piston. R is the vessel from which the air is to be ex- 
hausted, r and u are valves opening upward The action 
of the pump is as follows: 

On pushing the piston down, the air in C is compressed. 
This opens valve r allowing the confined air to escape 
above the piston. The piston is then raised making the 
space in C a partial vacuum. The pressure in R now being 
greater than in C, u is pushed up and the air from R 
rushes into C, until the pressure is equalized. On pushing 
down the piston again, valve u closes and the process is 
repeated until the pressure in R is no longer able to raise 
the value u. Some air pumps are so constructed that the 
valves are opened and closed automatically by the move- 
ment of the piston. With these pumps a higher degree of 
rarefaction can be obtained. 

Air is often partially exhausted from re- . 
ceivers or vessels by the use of a filter 
pump or aspirator. A stream of water 
flowing through a constriction causes a 
reduced pressure, draws in air and carries 
it away, and thus produces a partial 
vacuum. See Fig. 40 for a section of the 
device. 

61. The Condensing Pump. This is 
like the exhaust pump except that its 
valves are reversed. It is used in com- 
pressing illuminating gases into cylinders 
for use in lighting vehicles, stereopticons, Pintsch lights, 
gas light buoys, etc., and also for compressing air to 
operate air brakes, pneumatic hammers and drills, and 
for other uses. 

The common condensing pump is the kind used for 



WATER 



Fig. 40. An 
aspirator. 






68 PHYSICS 

inflating tires. (See Fig. 41.) In this, a loosely fitting 

metal piston is attached to a disc of leather somewhat 

larger than the cylinder. This device is called a cup valve. 

On raising the piston, air rushes in from the top past the 

valve, but on pushing the piston down, the valve is pressed 

tightly against the sides of the cylinder and prevents 

the escape of any air. The compressed air 

pushes open a valve on the tire and 

y enters it. This valve closes as soon as the 

pressure is lessened from outside. It is 

Jp gs== well to notice in all of these pumps that 

/? ^. two valves are used. One holds the air 

already secured while the other opens for 

Fig. 41. a new supply. Both valves are never 
Condens ing 
pump used in open at* the same time. 

inflating tires. 62# Water Pumps. The Common Lift 
Pump. This, the simplest pump for raising water, con- 
sists of a cylinder C (Fig. 42) connected by a pipe R to a 
supply of water as a cistern or well. A valve opening 
upward is placed at the bottom of the cylinder over the 
entrance to the pipe. In the cylinder is a tightly fitting 
piston connected by a rod to a lever for ease in action. 
The piston contains a valve opening upward. In oper- 
ating this pump water is usually first poured into the 
cylinder to "prime" it. This helps to close the valves 
and prevents air leaking past them. When the piston is 
lowered the lower valve closes, the air in the cylinder 
being compressed pushes the upper valve open and 
passes above the piston. On raising the piston the 
upper valve closes. This forms a partial vacuum in the 
cylinder. 

The air pressing on the surface of the water below forces 
the water and air that may be in the tube upward through 
the lower valve to fill this partial vacuum. 



MECHANICS OF GASES 



6 9 



When the cylinder becomes filled with water, this is 
lifted out on the up-stroke, whence its name, "lift pump." 
Since the atmospheric pressure at sea-level can only 
support a column of water about 34 ft. high, the lower 
valve must be within this distance of the water surface. 
In actual practice the limit is about 27 ft. In deeper 
wells, the cylinder and valves are placed so that they are 
within 25 or 27 ft. of the surface of the water in the well, 





J9 




^\X 


I 


I 


"^K 


i^bf 11 



Fig. 42. The common lift pump. 



Fig. 43. A force pump with 
an air chamber (.4) 



a long piston rod reaching above the surf ace of the ground 
and connected to a pump handle operates the piston. A 
discharge pipe extends from the cylinder to the surface of 
the ground above. 

63. The Force Pump. The force pump is used to 
deliver water under pressure either for spraying or to 
an elevated reservoir. The piston is solid, the second 
valve being placed at the entrance of the discharge pipe. 
(See Fig. 43.) The action is the same as that of the 
lift pump, with this exception; the piston in its down 



7o 



PHYSICS 



stroke forces the water out through the discharge pipe, 
the velocity depending upon the pressure exerted. 

A force pump is usually provided with an air chamber 
which is connected with the discharge pipe. On the down 
stroke of the piston, water is forced into the air chamber. 
This compresses the air it contains. The compressed 
air reacts and exerts pressure on the water forcing it out in 
a steady stream. 

Force pumps are used in deep wells, being placed at the 
bottom. 




Fig. 44. A steam pump used on a fire engine. 

The pumps used in city water works, fire engines, and 
all steam pumps, are force pumps. (See Fig. 44.) 

64. The Siphon. The siphon is a tube used to convey a 
liquid from one level over an elevation to a lower level by 
atmospheric pressure. It is used to remove liquids from 
tanks or vessels that have no opening at the bottom. 

The siphon cannot be completely understood until 
one has mastered the laws of the flow of liquids. The 
following is offered as an incomplete explanation of its 
behavior. Consider the siphon to be full of water and 



MECHANICS OF GASES 



71 



Fig. 



45. Cross-section 
of a siphon. 



closed at d (Fig. 45). Atmospheric pressure on a will 
hold the siphon full if ab does not exceed 34 feet. If 
d is opened the water falls out with a speed equal to 
that acquired in falling from the ^ 

level of a to that of d. This speed 
is acquired by all the water in the 
siphon and results in a drop in 
pressure throughout it. The pres- 
sure at a inside the siphon be- 
comes less than the pressure at 
the same level outside as soon as 
the water starts flowing. The water 
in the vessel then flows into the 
siphon and out at d. This flow con- 
tinues as long as there is a fall from 
the free surface of the water in the 
vessel to the outlet at d. 

65. The Cartesian Diver . This is a device which illus- 
trates at the same time transmission of pressure by liquids, 
Archimedes' principle, and compressibility of gases. 
It was invented by Des Cartes (1596- 
1650). As ordinarily made, it is a 
hollow glass image with a small opening 
in the foot. It contains air and water 
in such amounts that the average density 
of image and contents is slightly less 
than that of water. It is placed in a tall 
glass jar filled with water and covered 
with tightly stretched rubber tissue. (See 
Fig . 46 . ) By pressing on the rubber cover 
Fig. 46. The the diver may be made to sink, since 
the air and water transmit the pressure 
on the cover which compresses the air inside the figure 
admitting some water to it, thus making the diver more 




7 2 



PHYSICS 




dense than water. By varying the pressure it can be 
made to sink, rise, or remain stationary at will. 1 A small 
vial can be used instead of the image. 

66. Hydraulic Ram. The hydraulic ram (see Fig. 47) 
is an automatic device that is much used for raising water 
from springs to houses located on higher ground. Water 
flows through the pipe A through the opening at B. The 
pressure closes the valve at B. The increased pressure 

in the pipe due to the 
closing of B opens the 
valve C and some of the 
water flows into the air 
chamber D. This re- 
duces the, pressure 
against the valve B so 

Fig. 47.-Cross-section of a hydraulic ram. ^ k drQps and allows 

a little water to escape. Just as this happens, valve C 
closes. The pressure in the pipe then closes B and forces 
water past C. This action being continually repeated, 
the air in D becomes so compressed that it has elastic 
force enough to raise the water in a steady stream to a 
height of many feet. 

67. The Balloon. Since air is a fluid, Archimedes' 
principle applies to it as well as to liquids. Therefore 
any object in the air is lifted up by a force equal to the 
weight of the air it displaces. The object will rise, if it 
weighs less than this displaced air and will continue to 
rise until both weights are equal. 

The Balloon (Fig. 48) rises because it weighs less than 
the air it displaces, and therefore it is pushed up by the 
heavier air, the "lifting power" being the difference be- 
tween its weight and that of the air displaced. The 

x The position of a submarine in or under water is controlled in a 
similar manner. 



MECHANICS OF GASES 



73 



neck at the bottom is left open to allow for expansion 
of the gas. When the aeronaut wishes to descend, 
he opens a valve at the top allowing some of the gas to 
escape. 

Hydrogen is the lightest gas, weighing 0.09 kg. per cubic 
meter, and so gives the greatest lifting power, but as it is 




Fig. 48. Winner of international championship race, Paris, 1913. 



expensive to make, coal gas, density 0.75 kg. per cubic 
meter, is ordinarily employed. Helium has recently been 
used to fill military balloons because it cannot be set on fire. 



74 



PHYSICS 




Fig. 49. A parachute. 



The Parachute (Fig. 49) is an umbrella-shaped device 
for use in descending from a balloon. After falling a few 
seconds it opens, the large surface exposed to the air caus- 
ing it to descend slowly. The hole 
in the top keeps the parachute up- 
right by allowing the air to escape 
through it, thus relieving the pressure. 
68. The Air Brake. Compressed 
air is used to do work in many 
machines, such as pneumatic drills, 
hammers, and air brakes. The 
Westinghouse air brake (Fig. 50) 
uses air at a pressure of about 70 
lbs. to the square inch. The essential 
parts as shown are a reservoir R, 
the brake cylinder C and a triple valve V, placed under 
each car with an air pipe P, leading to the engine. This 
is connected to R by the triple valve V. When the pres- 
sure in P is reduced by the engineer or by accident, the 
triple valve operates so 
as to admit air from R 
into the cylinder C 
pushing the piston H 
to the left. H is con- 
nected to the brakes 
by levers which press 
the brake shoes 
strongly against the 
wheels. When the air 

pressure in P is restored FlG - 5o. Cross-section of a Westinghouse 
r air brake. 

the triple valve acts 

so as to permit the air in C to escape while R is filled 
again from P. The hissing sound heard when a train 
stops is caused by air escaping from cylinder C. The 




MECHANICS OF GASES 



75 



spring in C keeps the brakes from the wheels except 
when the " air is on." 

69. The Gas Meter. The gas meter consists of a 
box divided into two parts by a vertical partition (Fig. 
51). Two bellows are at- 
tached to this partition, one 
on each side. The valves 
that regulate the flow of gas 
to and from the bellows and 
the chambers A and D are 
opened and closed by levers 
connected with the bellows. 
These levers also operate the 
hands upon the dials. When 
the inlet to the bellows B 
is opened, the outlet of A is 
also opened. Gas entering B 
opens the bellows and forces 
the gas in A out into the 
house-pipe E. When B is 
full its inlet valve closes and 
its outlet valve opens. The 
inlet of A also opens and its 
outlet closes. Gas now flows 
into A, compressing the bel- 
lows and B, and forcing the 
gas from it into the house- 
pipe. At each filling of the bellows B there will be dis- 
placed from A and forced into the house-pipe as much 
gas as enters B. It is evident that at each emptying of 
B an equal amount of gas enters A. Thus we have A 
and B alternately filling and emptying as long as the 
gas burner is open. To have a continuous flow of gas 
in the house-pipes two pipes and two chambers are 




Fig. 51. Cross-section of a 
gas meter showing its construc- 
tion and action. 



7 6 



PHYSICS 



necessary, one being filled while the other is being 
emptied. 

Fig. 52 represents the 
dials upon a gas meter 
showing a reading of 54,- 
600 cu. ft. 

70. Centrifugal Pumps. 
Fluids, such as water and 
air, are often put in motion 
by devices called centrifugal pumps (see Art. 78) . These 
pumps contain a revolving part, like a wheel without a 
rim, whose spokes are replaced by thin blades. This re- 
volving part resembles the paddle wheel of some steam 




Fig. 52. Dials of a gas meter. 




Fig. S3- 



-A vacuum sweeper. {Courtesy of the Hoover Suction 
Sweeper Co.) 



boats and is enclosed in a case or cover having one 
opening at the rim and another opening on one side 
about the axle. 

When the wheel is rapidly revolved, the fluid is driven 
out with considerable force through the opening at the 
rim, while a partial vacuum is produced at the axle 
causing a rapid flow into the device at this point. 

This is the principle of the action of the vacuum cleaner. 



MECHANICS OF GASES 77 

Fig. 53 is a section of a vacuum sweeper showing the 
revolving wheel and the current of air passing into the 
wheel at the lower side and out of the rim of the case at 
the rear. 

Centrifugal water pumps work on the same principle 
and furnish a continuous flow of water, often large in 
volume and at considerable pressure. 

Important Topics 

i. Air pump. 6. Hydraulic ram. 

2. Condensing pump. 7. Balloon. 

3. Lift and force pumps. 8. Air brake. 

4. Siphon. 9. Gas meter. 

5. Cartesian diver. 10. Vacuum cleaner. 

Exercises 

1. Explain why smoke settles to the ground before storms. 

2. Why does the water rise in the suction pipe of a pump? 

3. Why is it easier to float in water when the lungs are filled with 
air? than when they are not filled? 

4. Why is it easier to swim in salt water than in fresh water? 

5. How are submarines made to sink? to rise to the surface? 

6. How can a fish rise or sink in water? 

7. Explain why a life preserver made of cork will enable a person 
to float. 

8. Hold the open hand out flat with the fingers together. Place 
underneath the fingers a piece of paper. Blow between the 
first and second fingers against the paper. As long as you blow 
hard the paper will not fall but will stick to the hand. Explain. 

9. Why does pressing the bulb of an atomizer force out the liquid 
in a fine spray? 

10. Why is air that contains a large amount of water vapor lighter 
than air that only contains a small amount? 

11. How are heights above sea-level ascertained by a barometer? 

12. Oil floats on water but sinks in alcohol. Explain. 

13. In a balloon the lower end is often open to the air. Why does 
not the gas escape and prevent the balloon from rising? 

14. How long will a balloon continue to rise? 



78 



PHYSICS 



15. If the pressure against the 8-in. piston of an air brake is 70 lbs. 
per square inch, how much force does the piston exert? 

16. The capacity of a balloon is 40,000 cu. ft. The weight of the 
balloon, car, etc., is 600 lbs.; specific gravity of the gas used is 
0.46 that of the air. Find how much weight the balloon can 
carry. 

17. The so-called Magdeburg hemispheres were invented by Otto 
von Guericke of Magdeburg, Germany. When the hemispheres 
(see Fig. 54) are placed in contact and the air exhausted it is 
found very difficult to pull them apart. Explain. 

18. Von Guericke's hemispheres had an inside diameter of 22 in. 
What force would be required to pull them apart if all the air 

were exhausted from them? (Find the atmos- 
pheric force on a circle, 22 in. in diameter.) 

19. Von Guericke made a water barometer whose 
top extended through the roof of his house. 
On the top of the water in* the tube was 
placed a wooden image. In fair weather the 
image appeared above the roof, but it de- 
scended before a storm. Explain. 

20. The balloon "Goodyear" (Fig. 48), which won 
the International championship race at Paris 
in 1913, has a capacity of 80,000 cu. ft. The 
gas bag weighs 653 lbs., the net 240 lbs. and 
the basket 92 lbs. How large a load can it 
carry when filled with hydrogen specific gravity 
0.069 (compared with air). 

Review Outline: Liquids and Gases 




Fig. 54 . 
Magdeb u rg 
hemispheres. 



Liquids: Force, pressure, and density. Floating and immersed 

bodies. 

Laws: Liquid force, F = A.h.d, Pascal's, Archimedes. 

Illustrations and Applications: 

;. .. Wa W.-Wi 

Specific gravity, p^r~jjT 



l -> Boyle's, PV = P'V 



Wa~W v 

Devices: Hydraulic press, air cushion, barometer mercurial and 
aneroid. Pumps, lift, force, vacuum, compression, centrifugal, 
balloon, siphon, etc. Construction and action of each. 



CHAPTER V 
FORCE AND MOTION 

(i) Force, How Measured and Represented 

71. Force. We have been studying various forces, 
such as air pressure, pressure in liquids, and the force of 
elasticity in solids, and have considered them simply as 
pushes or pulls. A more formal study of forces in general 
and of devices for representing and measuring them will 
be helpful at this point of the course. 

A force is that which tends to cause a change in the size 
or shape of a body or in its state of motion. In other words a 
force is a push or a pull. That is, force tends to produce 
distortion or change of motion in a body. Force itself 
is invisible. We measure it by the effect it produces. 
Forces are usually associated with the objects exerting 
them. Thus we speak of muscular force, air pressure, 
liquid pressure, the force of a spring, the force of the earth's 
attraction and so on. 

Forces are classified in various ways. 

I. With respect to the duration and steadiness of the 
force. 

(a) Constant, as the earth's attraction, (b) Impulsive, 
as the stroke of a bat on a ball, (c) Variable, as the force 
of the wind. 

II. With respect to the direction of the force. 

(a) Attractive, as the earth's attraction, (b) Repul- 
sive, as air pressure, liquid pressure, etc. 

72. Methods of Measuring Force. Since forces are 
measured by their effects which are either distortion or 
change of motion, either of these effects may be used to 

79 * 



8o 



PHYSICS 




measure them. For example, the force exerted by a 
locomotive is sometimes computed by the speed it can 
develop in a train of cars in a given time, or the force of 
the blow of a baseball bat is estimated by the distance the 
ball goes before it strikes the ground. 

The more common method of measuring 
force, however, is by distortion, that is, by 
measuring the change of shape of a body 
caused by the force. In doing this, use 
is made of Hooke's Law (Art. 32), in which 
it is stated that "within the limits of per- 
fect 'elasticity," changes of size or shape 
are directly proportional to the forces em- 
ployed. That isj twice as great a force will 
produce twice as great a change of shape 
and so on. 

A common contrivance using this prin- 
ciple is the spring balance (Fig. 55), with 
which all are familiar, as ice scales, meat 
scales, postal scales, etc. The object 
which changes shape in this device is a 
coiled spring contained in the case of the 
instrument. The balance is so constructed 
that when the spring is pulled out as far as 
possible it has not reached its limit of 
elasticity, since, if the spring were stretched so as to exceed 
its elastic limit, the index would not return to its first 
position on removing the load. (See Arts. 30-32.) 

73. Graphic Representation of Forces. A force is 
said to have three elements. These are (a) its point of 
application, (b) its direction, and (c) its magnitude. For 
example, if there is hung upon the hook of a spring balance 
a weight of 5 lbs., then we have: (a) its point of applica- 
tion on the hook of the balance, (b) its downward direction 







Fig. ss . A 
spring balance. 



FORCE AND MOTION 



8l 



and (c) its magnitude, or 5 lbs. These three elements 
may be represented by a line. Thus in Fig. 56a, a line 
AB is drawn as shown, five units long; A represents the 
point of application; B, the arrow head, shows the direc- 
tion; and the length of the line (five units) shows the magni- 
tude of the force. 

This is called a graphic representation since it represents 
by a line the quantity in question. If another weight of 
5 lbs. were hung from the 



first one, the graphic repre- 
sentation of both forces 
would be as in Fig. 566. 
Here the first force is repre- 
sented by AB as before, BC 
representing the second 
force applied. The whole 
line represents the resultant 
of the two forces or the result 
of their combination. If the 
two weights were hung one 
at each end of a short stick 



A 



B 
(a) 



A 



B 
(b) 



Mi 



A 



B 
(<0 



N 



D 



Fig. 56. Graphic representation 
of forces acting along the same or 
AC (Fig. 56c), and the lat- parallel lines. 

ter suspended at its center 

their combined weight or resultant would of course be 

applied at the center. The direction would be the same 

as that of the two weights. The resultant therefore is 

represented by ON. In order to exactly balance this 

resultant ON, a force of equal magnitude but opposite in 

direction must be applied at the point of application of 

ON, or O. OM then represents a force that will just 

balance or hold in equilibrium the resultant of the two 

forces AB and CD. This line OM therefore represents the 

equilibrant of the weights AB and CD. The resultant 

of two forces at an angle with each other is formed differ- 



82 PHYSICS 

ently, as in Fig. 57 a. Here two forces AB and AC ate 
at an angle with each other. Lay off at the designated 
angle the lines AB and AC of such length as will accurately 
represent the forces. Lay off BD equal to AC and CD 
equal to AB. The figure A BCD is then a parallelogram. 
Its diagonal AD represents the resultant of the forces 
AB and AC acting at the angle BAC. If BAC equals 90 

^n: >\b 



a b 

Fig. 57. Graphic representation of two forces acting (a) at a right angle, 
(b) at an acute angle. 

degrees or is a right angle, AD may be computed thus: 
AB* + BD 2 = AD\ Why? 

and AD = VjB 2 + BLP. 

This method of determining the resultant by computation 
may be used when the two forces are at right angles. 
(In any case, AD may be measured using the same scale 
that is laid off upon AB and AC, as shown in Fig. 57 b.) 
The three cases of combining forces just given may be 
classified as follows: The first is that of two forces act- 
ing along the same line in the same or opposite direction, as 
when two horses are hitched tandem, or in a tug of war. 
The second is that of two forces acting along parallel lines, in 
the same direction, as when two horses are hitched side by 
side or abreast. The third is that of two forces acting at 
the same point at an angle. It may be represented by the 
device shown in Fig. 58, consisting of two spring balances 



FORCE AND MOTION 



83 



suspended from nails at the top of the blackboard at A 
and B. A cord is attached to both hooks and is passed 
through a small ring at from which is suspended a 
known weight, W. Lines are drawn on the blackboard 
under the stretched cords, from O toward OA, OB, and OW 
and distances measured on each from O to correspond to 
the three forces as read on balance A and B and the 
weight W. Let a parallelogram be constructed on the 
lines measured off on OA and OB. Its diagonal drawn 
from will be found to 
be vertical and of the 
same length as the line 
measured on OW. The 
diagonal is the resultant 
of the two forces and 
OW is the equilibrant 
which is equal and oppo- 
site to the resultant. 

Again, the first case 
may be represented by a 

boat moving up or down Fig. 58. Experimental proof of par- 

. . allelogram of forces, 

a stream; the resultant 

motion being the combined effect of the boat's motion 

and that of the stream. The second, may be represented 

by two horses attached side by side to the same evener. 

The resultant force equals the sum of the two component 

forces. The third, may be represented by a boat going 

across a stream, the resultant motion being represented 

by the diagonal of the parallelogram formed by using the 

lines that represent the motion of the stream and of the 

boat. 

74. Units for Measuring Force. Force is commonly 

measured in units of weight: in pounds, kilograms, and 

grams. For example, we speak of 15 lbs. pressure per 




84 PHYSICS 

square inch and 1033.6 g. pressure per square centimeter 
as representing the air pressure. It should be noted here 
that the words pound, kilogram, and gram are used not 
only to represent weight or force but also the masses of the 
objects considered. Thus, one may speak of a pound- 
mass meaning the amount of material in the objept. 

It will help to avoid confusion if we reserve the simple 
terms "gram" and "pound" to denote exclusively an 
amount of matter, that is, a mass, and to use the full 
expression "gram of force" or "pound of force "whenever 
we have in mind the pull of the earth upon these masses. 
Or, one may speak of a pound-weight meaning the amount 
of attraction exerted by the earth upon the object. The 
same is true of gram-mass and gram-weight. .The mass of 
a body does not change when the body is transferred to 
another place. The weight, however, may vary, for on 
moving a body from the equator toward the poles of the 
earth the weight is known to increase. 

Important Topics 

1. Definition of force. 

2. Classification of forces, (a) Duration: constant, impulsive, 
variable, (b) Direction: attractive, repulsive. 

3. Methods of measuring force, (a) By distortion, (b) By change 
of motion. 

4. Graphic representation of forces: component, resultant, equi- 
librant. 

5. Three cases of combining forces. (1) Two forces acting on the 
same line. (2) Two forces acting in parallel lines. (3) Two 
forces acting at the same point at an angle. 

6. Units for measuring force, pound, gram. 

Exercises 

1. Name five natural forces. Which produce a tension? Which a 
pressure? 

2. How much can you lift? Express in pounds and kilograms. 



FORCE AND MOTION 85 

3. Show graphically the resultatnt of two forces at right angles, one 
of 12 lbs., the other of 16 lbs. What is the magnitude of this 
resultant? Then determine the answer, first by measurement 
and then by computation. Which answer is more accurate? 
Why? 

4. Represent by a parallelogram the two forces that support a person 
sitting in a hammock and draw the line representing the resultant. 

5. Find graphically the resultant of the pull of two forces, one of 
500 lbs. east and one of 600 lbs. northwest. 

6. Determine the equilibrant of two forces, one of 800 lbs. south and 
one of 600 lbs. west. 

7. Would the fact that weight varies on going from the equator 
to either pole be shown by a spring balance or a beam balance? 
Explain. 

(2) Motion. Newton's Laws of Motion 

75. Motion a Change of Position. Motion is defined 
as a continuous change in the position of a body. The posi- 
tion of a body is usually described as its distance and direc- 
tion from some fixed point. Thus a man on a boat may be 
at rest with respect to the boat and moving with respect 
to the earth. Or, if he walks toward the stern as fast- 
as the boat moves forward, he may keep directly over a 
rock on the bottom of the lake and hence not be mov- 
ing with reference to the rock and yet be in motion with 
respect to the boat. Motion and rest, therefore, are 
relative terms. The earth itself is in motion in turning 
on its axis, in moving along its orbit, and in following 
the sun in its motion through space. Motions are classi- 
fied in several ways : 

(A) Modes of Motion 

1. Translation. A body is said to have motion of 
translation when every line in it keeps the same direction. 

2. Rotation. A body has motion of rotation when it 



86 PHYSICS 

turns upon a fixed axis within the body, as a wheel upon 
its axle or the earth upon its axis. 

3. Vibration or Oscillation. A body is said to have 
vibratory or oscillatory motion when it returns to the 
same point at regular intervals by reversals of motion 
along a given path, e.g., a pendulum. 

(B) Direction of Motion 

1 . Rectilinear. A body has rectilinear motion when its 
path is a straight line. Absolute rectilinear motion does 
not exist, although the motion of a train on a straight 
stretch of track is nearly rectilinear. 

2. Curvilinear. A body has curvilinear motion when 
its path is a curved line, e.g., the path of a thrown ball. 

(C) Uniformity of Motion 

1. Uniform. A body has uniform motion when its 
speed and direction of motion do not change. Uniform 
motion for extended periods is rarely observed. A train 
may cover, on an average, 40 miles per hour but during 
each hour its speed may rise and fall. 

2. Variable. A body has variable motion when its 
speed or direction of motion is continually changing. Most 
bodies have variable motion. 

3. Accelerated. A body has accelerated motion when 
its speed or direction of motion continually changes. 

If the speed changes by the same amount each second, 
and the direction of motion does not change the motion is 
said to be uniformly accelerated, e.g., a falling body. 

Uniformly accelerated motion will be studied further 
under the topic of falling bodies. 

Velocity is the rate of motion of a body in a given direction. 
For example, a bullet may have a velocity of 1300 ft. a 



FORCE AND MOTION 87 

second upwards. Acceleration is the rate of change of 
velocity in a given direction, or the change of velocity in a 
unit of time. A train starting from a station gradually 
increases its speed. The gain in velocity during one 
second is its acceleration. When the velocity is decreas- 
ing, as when a train is slowing down, the acceleration is 
opposite in direction to the velocity. A falling body falls 
faster and faster. It has downward acceleration. A ball 
thrown upward goes more and more slowly. It also has 
downward acceleration. 

76. Momentum. It is a matter of common observa- 
tion that a heavy body is set in motion with more difficulty 
than a light one, or if the same force is used for the same 
length of time upon a light and a heavy body, 1 the light 
body will be given a greater velocity. This observation 
has led to the calculation of what is called the "quantity 
of motion" of a body, or its momentum. It is computed 
by multiplying the mass by the velocity. If the C. G. S. 
system is used we shall have as the momentum of a 12 g. 
body moving 25 cm. a second a momentum of 12 X 25 
or 300 C. G. S. units of momentum. This unit has no 
name and is therefore expressed as indicated above. The 
formula for computing momentuin is : M = mv. 

Newton's Laws of Motion 

77. Inertia, First Law of Motion. One often observes 
when riding in a train that if the train moves forward 
suddenly the passengers do not get into motion as soon 
as the train, and apparently are jerked backward. While 
if the train is stopped suddenly, the passengers tend to 
keep in motion. This tendency of matter to keep moving 
when in motion and to remain at rest when at rest is 

'By a light body is meant one of small mass, a heavy body possess- 
ing much greater mass. 



88 PHYSICS 

often referred to as the property of inertia. Newton's 
first law ot motion, often called the law of inertia, describes 
this property of matter as follows : 

Every body continues in a state of rest or of uniform 
motion in a straight line unless it is compelled to change 
that state by some external force. This means that if an 
object like a book is lying on a table it will remain there 
until removed by some outside force. No inanimate 
object can move itself or stop itself. If a ball is thrown 
into the air it would move on forever if it were not for 
the force of attraction of the earth 
and the resistance of the air. 

It takes time to put a mass into 
motion, a heavy object requiring 
more time for a change than a light 
object. As an example of this, note 
the movements of passengers in a 
Fig. 59. The ball re- street car when it starts or stops 

mains when the card is , , , . ,, ... ,. . 

driven away. suddenly. Another illustration of 

the law of inertia is the so-called 
"penny and card" experiment. Balance a card on the end 
of a finger. Place on it a coin directly over the finger, 
snap the card quickly so as to drive the card from beneath 
the coin. The coin will remain on the ringer. (See Fig. 

59-) 

According to Newton's first law of motion a moving 
body which could be entirely freed from the action of all 
external forces would have uniform motion, and would 
describe a perfectly straight course. The curved path 
taken by a baseball when thrown shows that it is acted 
upon by an outside force. This force, the attraction of 
the earth, is called gravity. 

78. Curvilinear Motion. Curvilinear motion occurs 
when a moving body is pulled or pushed away from a 




Sir Isaac Newton (1642-1727) 
Professor of mathematics at 
Cambridge university; discovered 
gravitation; invented calculus; 
announced the laws of motion; 
wrote the Principia; made many 
discoveries in light. 





Sir Isaac Newton 
"By Permission of the Berlin Photo- 
graphic Co., New York." 



Galileo Galilei (1564-1642). 
Italian. "Founder of experi- 
mental science"; "Originator of 
modern physics"; made the first 
thermometer; discovered the laws 
of falling bodies and the laws of 
the pendulum; invented Galilean 
telescope. 



Galileo Galilei 
' By Permission of the Berlin Photo- 
graphic Co., New York. " 



FORCE AND MOTION 



91 



straight path. The pull or push is called centripetal 
(center-seeking) force. A moving stone on the end of a 
string when pulled toward the hand moves in a curve. 



SIMPLE CREAM SCREW' 

ADJUSTMENT 



SIGHT FEED LUBRICAT 
(SOLE OIL SUPaY) 



CENTER BALANCED BOWL, 



SPLIT-WING TUBULAR 
OR FEEDING SHAFT 



ONE PIECE DETACHED SPINDLE 



SEAMLESS ANTI-SPLASH 
SANITARY SUPPLY CAN 



SANITARY FAUCET 
EXTRA HEAVY TINWARE 
REVERSIBLE ROAT 



HIGH BEARING CASE PROTECTING; 
GEARS FROM MILK AND WATER 



HELICAL TOOTH SPUR. PINIOi 
AND WORM WHEEL GEARS 



BRONZE REVERSIBLE WORM WHEa 
FRAME JOINING SCREW 
OPEN. SANITARY 




Fig. 60. Cross-section of the DeLaval cream separator. 

If the string is released the stone moves in a tangent to the 
curve. The string pulls the hand. This phase of the pull 
is called centrifugal force. The centripetal force is the 
pull on the stone. Centripetal and centrifugal force 



Q2 PHYSICS 

together cause a tension in the string. Examples of cur- 
vilinear motion are very common. The rider and horse 
in a circus ring lean inward in order to move in a curve. 
The curve on a running track in a gymnasium is "banked " 
for the same reason. Mud flying from the wheel of a 
carriage, the skidding of an automobile when passing 
rapidly around a corner, and sparks flying from an emery 
wheel, are illustrations of the First Law of Motion. 

Cream is separated from milk by placing the whole 
milk in a rapidly revolving bowl, the cream being lighter 
collects in the center and is thrown off at the top. (See 
Fig. 60.) Clothes in steam laundries are dried by a 
centrifugal drier. In amusement parks many devices 
use this principle. (See centrifugal pumps, Art. 70.) 

79. The Second Law of Motion, sometimes called the 

law oj momentum, leads to the measurement of force, 

by the momentum or the quantity of motion, produced 

by it. The law is stated as follows: 

Change of motion, 

Q ; Q or momentum, is pro- 

portional to the acting 
Fig. 61. The two balls reach the floor x j . , 7 

at the same time. force and takes P lace m 

the direction in which 
the force acts. In other words, if two or more forces act at 
the same instant upon a body each produces the same 
effect that it would if acting alone. If a card be supported 
on two nails driven horizontally close together into an 
upright board (see Fig. 61), and two marbles be so placed 
on the ends as to balance each other, when one marble is 
snapped horizontally by a blow, the other will fall. Both 
reach the floor at the same time. The two balls are 
equally pulled down by the earth's attraction and strike 
the ground at the same time, though one is shot sidewise, 
and the other is dropped vertically. 



FORCE AND MOTION 93 

As gravity is a constant force, while the blow was only a 
momentary force, the actual path or resultant motion 
will be a curved line. 

The constant relation, between the acting force and the 
change of momentum it produces in a body, has led to 
the adoption of a convenient C. G. S. unit of force called 
the dyne. The dyne is that force which can impart to a 
mass of one gram a change' of velocity at the rate of one centi- 
meter per second every second. This definition assumes 
that the body acted upon is free to move without hindrance 
of any kind, so that the acting force has to overcome only 
the inertia of the body. However, the law applies in every 
case of application of force ; so that each force produces 
its full effect independently of other forces that may be 
acting at the same time upon the body. 

80. Newton's Third Law. This law has been experi- 
enced by everyone who has jumped from a rowboat near 
the shore. The muscular action that pushes the body 
forward from the boat also pushes the boat backward, 
often with awkward results. The law is stated: To 
every action, there is always an opposite and equal reaction, 
or the mutual actions of any two bodies are always equal 
and opposite in direction. Many illustrations of this law 
are in every one's mind: a stretched rope pulls with' 
the same force in one direction as it does in the opposite 
direction. If a bat hits a ball, the ball hits the bat with an 
equal and opposite force. The third law is therefore some- 
times called the law of reaction. When a weight is hung 
upon a spring balance the action of the weight pulls down 
the spring until it has stretched sufficiently (Hooke's 
Law) to produce an elastic reaction that equals and hence 
supports the weight. When a man stands at the center 
of a plank supported at its ends, the action of the man's 
weight bends the plank until the elastic force developed 



94 PHYSICS 

in the plank equals the weight applied. Further, when a 
train or a wagon is on a bridge the bridge yields until it 
has developed an elastic reaction equal to the weight 
applied. If a person stands in the center of a room, the 
floor beams yield until the third law is satisfied. In fact, 
whenever a force acts, a contrary equal force always acts. 

81. Stress and Strain. A pair of forces that constitute 
an action and a reaction is called a stress. The two forces 
jlxq two parts of one stress. If the two forces act away 
irom each other, as in the breaking of a string, the stress 
is called a tension, but if they act toward each other as 
in crushing anything, the stress is called a pressure. In 
order for a body to exert force it must meet with resistance. 
The force exerted is never greater than the resistance en- 
countered. Thus one can exert but little force upon a 
feather floating in the air or upon other light objects. A 
fast moving shot exerts no force unless it encouters some 
resistance. 

Forces, then, are always found in pairs. Thus to break 
a string, to stretch an elastic band, to squeeze a lemon, one 
must exert two equal and opposite forces. Such a thing 
as a single force acting alone is unknown. Usually, how- 
ever, we give our attention mainly to one of the forces and 
ignore the other. When a force acts upon a body the 
change of shape or size resulting is called a strain. 
Hooke's law (Art. 32) is often expressed as follows: "The 
strain is proportional to the stress," e.g., the stretch of the 
spring of a spring balance is proportional to the load placed 
upon it. 

Important Topics 

1. Motion a change of position. Kinds of motion. 

2. Newton's laws of motion. 

3. Momentum. 

4. Inertia. First law of motion. Curvilinear motion. 



FORCE AND MOTION 95 

5. Second law of motion. 

6. Third law of motion. Action and reaction, stress and strain. 

Exercises 

1 Mention three illustrations of the third law, different from those 
given. 

2. A rifle bullet thrown against a board standing upon edge will 
knock it down; the same bullet fired at the board will pass 
through it without disturbing its position. Explain. 

3. A hammer is often driven on to its handle by striking the end | 
of the latter. Explain. 

4. Consider a train moving 60 miles an hour, with a gun on the 
rear platform pointing straight backward. If a ball is fired from 
the gun with a speed of 60 miles an hour, what will happen to 
the ball? 

5. Could one play ball on the deck of an ocean steamer going 25 
miles an hour without making allowance for the motion of the 
ship? Explain. 

6. On a railroad curve, one rail is always higher. Which? Why? 

7. Why can a small boy when chased by a big boy often escape by 
dodging? 

8. Will a stone dropped from a moving train fall in a straight line? 
Explain. 

9. A blast of fine sand driven against a sheet of glass soon gives it 
a rough surface. Explain. 

10. Explain the use of fly-wheels in steadying the motion of ma- 
chinery (for example, the sewing machine). 

u. Is it easier to walk to the front or rear of a passenger train 
when it is stopping? Why? 

12. Why does lowering the handles of a wheel-barrow on the instant 
of striking make it easier to go over a bump? 

13. Why should a strong side wind interfere with a game of tennis? 
How can it be allowed for? 

14. On which side of a railroad track at a curve is it the safer to 
walk while a train is passing? Why? 

15. Why does a bullet when fired through a window make a clean 
round hole in the glass, while a small stone thrown against the 
window shatters the glass? 

16. A tallow candle can be fired through a pine board. Why? 



96 PHYSICS 

17. In cyclones, straws are frequently found driven a little distance 
into trees; why are the straws not broken and crushed instead 
of being driven into the tree unbroken? 

18. A bullet weighing one-half oz. is fired from a gun weighing 
8 lb. The bullet has a velocity of 1800 ft. per second. Find 
the velocity of the "kick" or recoil of the gun. 

19. When football players run into each other which one is thrown 
the harder? Why? 

20. A railroad train weighing 400 tons has a velocity of 60 miles 
per hour. An ocean steamer weighing 20,000 tons has a veloc- 
ity of one half mile per hour. How do their momenta compare? 

2X. Why is a heavy boy preferable to a lighter weight boy for a 
football team? 

22. Why does a blacksmith when he desires to strike a heavy blow, 
select a heavy sledge hammer and swing it over his head? 

23. Why does the catcher on a baseball team wear a padded glove? 

(3) Resolution of. Forces 

82. Resolution of Forces. We have been studying the 
effect of forces in producing motion and the results of com- 
bining forces in many ways ; in the same line, in parallel lines, 
and in diverging lines. Another case of much interest and 
importance is the determination of the effectiveness of a force 
in a direction different from the one in which it acts. This 
case which is called resolution of jorces is frequently used. 
To illustrate : one needs but to recall that a sailor uses this 
principle in a practical way whenever he sails his boat in 
any other direction than the one in which the wind is 
blowing, e.g., when the wind is blowing, say from the north, 
the boat may be driven east, west, or to any point south 
between the east and west and it is even possible to beat 
back against the wind toward the northeast or northwest. 
Take a sled drawn by a short rope with the force applied 
along the line AB (see Fig. 62) ; part of this force tends to 
lift the front of the sled as AC and a part to draw it for- 
ward as AD. Hence not all of the force applied along 



FORCE AND MOTION 



97 



AB is used in drawing the sled forward. Its effectiveness 
is indicated by the relative size of the component AD 
compared to AB. 

The force of gravity acting upon a sphere that is resting 
on an inclined plane may be readily resolved into two com- 
ponents, one, the 

effective component, 

as OR, and the other, 
the non-effective as 
OS. (See Fig. 63.) 
If the angle ACB is 




Fig. 62. AD is the effective component. 
30 degrees, AB equals 

3^ of AC and OR equals ^ of OG, so that the speed of the 
sphere down the plane developed in 1 second is less than 
(about one-half of) the speed of a freely falling body de- 
veloped in the same time. Why is OS non-effective? 

Direction of Flight 




Fig. 63. The effective component is OR. 



Fig. 64. Resolution 
of the forces acting on an 
aeroplane. 



83. The Aeroplane. The aeroplane consists of one or 
two frames ABCD (see Fig. 64), over which is stretched 
cloth or thin sheet metal. It is driven through the air by 
a propeller turned by a powerful gasoline motor. This 
has the effect of creating a strong breeze coming toward 
the front of the aeroplane. As in the case of the sail- 
boat a pressure is created at right angles to the plane 
along GF and this may be resolved into two components 



9 8 



PHYSICS 



as GC and GE, GC acting to lift the aeroplane vertically 
and GE opposing the action of the propeller. Fig. 65 
represents the Curtis Flying Boat passing over the Detroit 



river. 




The Curtis hydroplane. 



Exercises 

1. If a wagon weighing 4000 lbs. is upon a hill which rises 1 ft. in 6, 
what force parallel to the hill will just support the load? (Find 
the effective component of the weight down the hill.) 

2. If a barrel is being rolled up a 16-ft. ladder into a wagon box 3 ft. 
from the ground, what force will hold the barrel in place on the 
ladder, if the barrel weighs 240 lbs. Show by diagram. 

3. Show graphically the components into which a man's push upon 
the handle of a lawn mower is resolved. 

4. Does a man shooting a flying duck aim at the bird? Explain. 

5. What are the three forces that act on a kite when it is " standing " 

in the air? 

6. What relation does the resultant of any two of the forces in prob- 
lem five have to the third? 



FORCE AND MOTION 



99 



^ i === t@?gjr>@ 



7. Into what two forces is the weight of a wagon descending a hill 
resolved? Explain by use of a diagram. 

8. A wind strikes the sail of a boat at an angle of 60 degrees to the 
perpendicular with a pressue of 3 lbs. per square foot. What is 
the effective pressure, perpendicular to the sail? What would 
be the effective pressure when it strikes at 30 degrees? 

9. How is the vertical component of the force acting on an aero- 
plane affected when the front edge of the plane is elevated? 
Show by diagram. 

(4) Moment of Force and Parallel Forces 

84. Moment of Force. In the study of motion we found 
that the quantity of motion is called momentum and is 
measured by the product of the mass times the velocity. In 
the study of parallel forces, A-B<r- 

especially such as tend to pro- 
duce rotation, we consider a 
similar quantity. It is called 
a moment of force, which is the 
term applied to the effective- t ynrnmc hlR 

ness of a force in producing Fig. 66. The moments about S 

change of rotation. It is are equal, 

also measured by the product of two quantities; One, 
the magnitude of the force itself, and the other, the perpen- 
dicular distance from the axis about which the rotation 
takes place to the line representing the direction ofthejorce. 
To illustrate: Take a rod, as a meter stick, drill a hole 
at S and place through it a screw fastened at the top of 
the blackboard. Attach by cords two spring balances 
and draw to the right and left, A and B as in Fig. 66. 
Draw out the balance B about half way, hold it steadily, 
or fasten the cord at the side of the blackboard, and read 
both balances. Note also the distance AS and BS. Since 
the rod is at rest, the tendency to rotate to the right and 
left must be equal. That is, the moments of the forces 



IOO PHYSICS 

at A and B about S are equal. Since these are computed 
by the product of the force times the force arm, multiply 
B by BS and A by AS and see if the computed moments 
are equal. Hence a force that tends to turn or rotate a body to 
the right can be balanced by another of equal moment that 
acts toward the left. 

85. Parallel Forces. Objects are frequently supported 
by two or more upward forces acting at different points 
and forming in this way a system of parallel forces; as 
when two boys carry a string of fish on a rod between 

them or when a bridge is 
r-fj \ tv\ supported at its ends. The 

principle of moments just de- 
Fig. 67.-L.aw ^parallel forces scribed aids fa determining 

the magnitude of such forces 
and of their resultant. To illustrate this take a 
wooden board 4 in. wide and 4 ft. long of uniform 
dimensions. (See Fig. 67.) Place several screw hooks 
on one edge with one set at O where the board will 
hang horizontally when the board is suspended there. 
Weigh the board by a spring balance hung at O. This 
will be the resultant in the following tests. Now hang 
the board from two spring balances at M and N and read 
both balances. Call readings / and f . To test the forces 
consider if as a fixed point (see Fig. 67) and the weight 
of the board to act at O. Then the moment of the weight 
of the board should be equal the moment of the force at 
N since the board does not move, or w times OM equals 
f times NM. If N is considered the fixed point then the 
moment of the weight of the board and of / with reference 
to the point N should be equal, or w times ON = / times NM. 
Keeping this illustration in mind, the law of parallel forces 
may be stated at follows : 1 . The resultant of two parallel 
forces acting in the same direction at different points in a 



FORCE AND MOTION IOI 

body is equal to their sum and has the same direction as the 
components. 

The moment of one of the components about the point of 
application of the other is equal and opposite to the moment 
of the supported weight about the other. 

Problem. If two boys carry a string of fish weighing 40 lbs. on 
a rod 8 ft. long between them, what force must each boy exert if 
the string is 5 ft. from the rear boy? 

Solution. The moment of the 
force F exerted about the opposite 
end by the rear boy is F X 8. The 
moment of the weight about the 
same point is 40 X (8 5) = 120. 
Therefore F X 8 = 120, or F = 15, 



the force exerted by the rear boy. jr IG 5s. a couple. 

The front boy exerts a force of F 

whose moment about the other end of the rod is F X 8. The 
moment of the weight about the same point is 40 X 5 = 200. 
Since the moment of F equals this, 200 = F X 8, orF = 25. Hence 
the front boy exerts 25 lbs. and the rear boy 15 lbs. 

86. The Couple. If two equal parallel forces act upon 
a body along different lines in opposite directions, as in Fig. 
68, they have no single resultant or there is no one force 
that will have the same effect as the two components 
acting together. A combination of forces of this kind is 
called a couple. Its tendency is to produce change of rota- 
tion in a body. An example is the action upon a compass 
needle which is rotated by a force which urges one end 
toward the north and by an equal force which urges the 
other end toward the south. v 

Important TopiGS 

1. Moment of force, how measured. 

2. Parallel forces. 

3. The two laws of parallel forces. 

4. The couple. 



102 



PHYSICS 



Exercises 

1. Show by diagram how to arrange a three-horse evener so that 
each horse must take one-third of the load. 

2. Two boys support a io-ft. pole on their shoulders with a 40-lb. 
string of fish supported from it 4 ft. from the front boy. What 
load does each boy carry? Work by principle of moments. 

3. If two horses draw a load exerting a combined pull of 300 lbs., 
what force must each exert if one is 28 in. and the other is 32 
in. from the point of attachment of the evener to the load. 

4. A weight of 100 lbs. is sus- 
pended at the middle of a rope 
ACB 20 ft. long. (See Fig. 69.) 
The ends of the rope are fast- 
ened at points A and B at the 





Fig. 69. 



Forces acting 
stretched rope. 



upon a 



Fig. 70. A crane with horizon- 
tal tie. 



same height. Consider D as the center of the line AB. 
What is the tension of the rope when CD is 3 ft.? When 
CD is 1 ft.? When CD is 1 in.? 

5. A crane is set up with the tie horizontal. (See Fig. 70.) If 1000 
lbs. is to be lifted, find the tie stress and the boom stress if the 
boom angle is 30 degrees? If 45 degrees? 60 degrees? 

6. A ball is placed on a plane inclined at an angle of 30 degrees 
to the horizontal. What fraction of its weight tends to cause 
motion down the plane? What effect does the other component 
of the weight have? Why? 

7. A person weighing 1 50 lbs. is lying in a hammock. The distance 
between the supports is 1 5 ft. The hammock sags 4 ft. What 
is the tension in the supports at each end? What is the tension 
when the sag is only 1 ft. ? 




FORCE AND MOTION 103 

8. A ladder 30 ft. long and weighing 80 lbs. leans against the side 
of a building so that it makes an angle of 30 degrees with the 
building. Find the direction and magnitude of the component 
forces on the ground and at the building. 

9. A traveling crane 50 ft. long weighing 10 tons moves from 
one end of a shop to the other, at the same time a load of 4000 
lbs. moves from end to end 

of the crane. Find the pres- C 

sure of the trucks of the 

crane on the track when the 

load is at a distance of 5, 10, 

15, and 25 ft. from either end. ^ I ft 

10. Resolve a force of 500 lbs. FlG 7I _ A truss< 
into two components at right 

angles to each other, one of which shall be four times the 
other. 

11. A truss (see Fig. 71), carries a load of 1000 lbs. at C. Find the 
forces acting along AC, BC, and AB. If AC and BC are each 
12 ft. and AB 20 ft., which of these forces are tensions and 
which are pressures? 

(5) Gravitation and Gravity 

87. Gravitation. Gravitation is the force of attraction 
that exists between all bodies of matter at all distances. 
This attraction exists not only between the heavenly 
bodies, the stars and planets, etc., but is also found be- 
tween bodies on the earth. A book attracts all objects 
in a room and outside of a room as well, since its weight 
shows that it is attracted by the earth itself. The gravi- 
tational attraction between ordinary bodies is so slight 
that it requires careful experiments to detect it. In fact, 
it is only when one of the attracting bodies is large, as 
for example the earth, that the force becomes considerable. 
Careful studies of the motions of the heavenly bodies, 
especially of that of the moon in its orbit about the earth, 
led Sir Isaac Newton to the statement of the law of gravi- 
tation which is well expressed in the following statement: 



104 PHYSICS 

88. Law of Gravitation. Every particle of matter in the 
universe attracts every other particle with a force that is 
directly proportional to the product of their masses and 
inversely proportional to the square of the distance between 
them. 

The law may be separated into two parts, one referring 
to the masses of the bodies concerned, the other to the 
effect of the distance between them. The first part is 
easily understood since we all know that two quarts of 
milk will weigh just twice as much as one quart. To 
illustrate the second part of the law, suppose that the moon 
were removed to twice its present distance from the earth, 
then the attraction between the earth and the moon would 
be one-Jourth its present attraction. If removed to three 
times its present distance, the attraction would be one- 
ninth, etc. 

The attraction of the earth for other bodies on or near 
it is called gravity. The weight of a body is the measure 
of the earth's attraction for it; or it is the force of gravity 
acting upon it. Newton's third law of motion states 
that every action is accompanied by an equal and opposite 
reaction (Art. 80). Hence, the attraction of the earth 
for a book or any other object is accompanied by an equal 
attraction of the book for the earth. 

89. Weight. In advanced physics it is proved that a 
sphere attracts as if it were concentrated at its center. 
Thus if the earth's radius be considered as 4000 miles, 
then a body 4000 miles above the earth's surface would 
be 8000 miles above the earth's center, or twice as far from 
the center of the earth as is a body upon the earth's surface. 
A body then 4000 miles above the earth's surface will 
weigh then but one-fourth as much as it will at the surface 
of the earth. 

Since the earth is flattened at the poles, the surface at 



FORCE AND MOTION 105 

the equator is farther from the center of the earth than 
at points north or south. Thus a body weighing i lb. 
at the equator weighs 1.002 lb. at Chicago, or about 
1/500 more. The rotation of the earth also affects the 
weight of a body upon it so that at the equator the weight 
of a body is 1/289 less than at the pole. Both effects, 
that of flattening and of rotation, tend to diminish the 
weight of bodies at the equator, so that a body at the 
latter place weighs about 1/192 less than at the poles. 

In studying the effect of the earth's gravity, the following illus- 
tration will be helpful: Imagine an open shaft a mile square extend- 
ing through the earth. What would happen to a stone thrown into 
the shaft? At first it would have the attraction of the whole earth 
drawing it and continually increasing its speed downward. As it 
descends from the surface, the pull toward the center grows less and 
less. Halfway to the center the body has lost half its weight. 
When the stone reaches the center, the pull in all directions is the 
same, or in other words, it has no weight. It would, however, con- 
tinue moving rapidly on account of its inertia, and as it continues 
on from the center, the greater part of the earth being left behind, 
the attraction pulling toward the center will gradually stop it. It 
will then fall again toward the center and be stopped again after 
passing it, and after repeatedly moving up and down will finally come 
to rest at the center of the earth. At this pointit will be found to be 
a body without weight since it is pulled equally in all directions by 
the material of the earth. What force brings the body to rest? 

90. Center of Gravity. A body is composed of a great 
many particles each of which is pulled toward the center 
of the earth by the force of gravity. A single force that 
would exactly equal the combined effect of the pull of the 
earth for all the particles of a body would be their resultant. 
The magnitude of this resultant is the weight of the body. 
The direction of this resultant is in a line passing toward 
the earth's center, while the point of application of this 



106 PHYSICS 

resultant is called the center oj gravity of the body. The 
center of gravity of a body may also be briefly defined as 
the point about which it may be balanced. As the location 
of this point depends upon the distribution of matter in 
the body, the center of gravity is also sometimes called 
the center oj mass of the body. 
The earth's attraction for a body is considered for the 
sake of simplicity, not as a multitude 
of little forces, but as a single force 
applied at its center of gravity. To 
find the center of gravity of a body 
find two intersecting lines along which 
it balances, see Fig. 72, and the center 
of gravity will be at the intersection. A 
ter of gravity is at the vertical line through this point is some- 
intersection of the t i mes ca n e d the line of direction of the 
lines of direction. t ' ' 

weight. 

91. Equilibrium of Bodies. Equilibrium means equally 
balanced. A body at rest or in uniform motion is then in 
equilibrium. An object is in equilibrium under gravity 
when a vertical line through its center of gravity passes 
through the point of support. A trunk is an example of a 
body in equilibrium since a vertical line from its center of 
gravity falls within the base formed by the area upon 
which it rests. Work will be necessary to tip the trunk 
from its position. The amount of work required will 
depend upon the weight of the body and the location of 
the center of gravity. 

92. Kinds of Equilibrium. (a) Stable. A body is in 
stable equilibrium under gravity if its center of gravity 
is raised whenever the body is displaced. It will return to 
its first position if allowed to fall after being slightly dis- 
placed. In Fig. 73, a and b if slightly tipped will return 
to their first position. They are in stable equilibrium. 



FORCE AND MOTION 



107 



Other examples are a rocking chair, and the combination 
shown in Fig. 74. 




Fig. 73. Stable equilibrium. 

(b) Unstable. A body is in unstable equilibrium under 
gravity if its center of gravity is lowered whenever the 
body is slightly displaced. It will fall farther from its first 
position. A pencil balanced 
on its point or a broom 
balanced on the end of the 
handle are in unstable equili- 
brium. The slightest dis- 
turbance will make the line 
of direction of the weight fall 

OUtside Of (away from) the FlG - 74- An example of stable 
... . *_,; N equilibrium. Why? 

point of support (rig. 75 a). 

(c) Neutral. A body is in neutral equilibrium if its 
center of gravity is neither raised nor lowered whenever 
the body is moved. Familiar examples are a ball lying 






a b 

Fig. 75. Unstable equilibrium a, neutral equilibrium b. 

on a table (Fig. 756) and a wagon moving on a level street 
(referring to its forward motion). 



io8 



PHYSICS 



A 
Fig. 76. 



B 



-B is more stable than A . 



93. Stability. When a body is in stable equilibrium, 

effort must be exerted to overturn it, and the degree of 

stability is measured by the effort required to overturn it. 

To overturn a body, it must be moved so that the vertical 
,- N line through its center 

of gravity will pass out- 
side of its supporting 
base. This movement 
in stable bodies neces- 
sitates a raising of the 
center of gravity. The 
higher this center of 
gravity must be raised 
in overturning the body, 

the more stable it is, e.g., see Fig. 76. Thus a wagon on a 

hillside will not overturn until its weight falls outside of 

its base, as in Fig. 77 B The stability of a body depends 

upon the position of its center of gravity and the area of 

its base. The lower the 

center of gravity and the 

larger the base, the more 

stable the body. What 

means are employed to 

give stability to bodies, 

in every-day use (such 

as clocks, ink-stands, 

pitchers, vases, chairs, 

lamps, etc). ? FlG - 77- 5 will overturn; A will not. 

Important Topics 

1. Gravitation; law of gravitation, gravity, weight. 

2. Center of gravity. 

3. The three states of equilibrium. Stability. 




FORCE AND MOTION 109 

Exercises 

1. Why is a plumb-line useful in building houses? 

2. What is the center of gravity of a body? 

3. Explain the action of a rocking chair that has been tipped 
forward. 

4. Is the stability of a box greater when empty or when filled with 
sand? Explain. 

5. How can you start yourself swinging, in a swing, without- touch- 
ing the ground? 

6. Is the center of gravity of the beam of a balance above, below, or 
at the point of a support? How did you find it out? 

7. Why are some ink bottles cone shaped with thick bottoms? 

8. Would an electric fan in motion on the rear of a light boat move 
it ? Would it move the boat if revolving under water ? Explain. 

9. What turns a rotary lawn sprinkler? 

10. Why, when you are standing erect against a wall and a coin is 
placed between your feet, can you not stoop and picket up 
unless you shift your feet or fall over? 

11. What would become of a ball dropped into a large hole bored 
through the center of the earth? 

12. When an apple falls to the ground, does the earth rise to meet it? 

13. How far from the earth does the force of gravity extend? 

14. Why in walking up a flight of stairs does the body bend forward? 

15. In walking down a steep hill why do people frequently bend 
backward? 

16. Why is it so difficult for a child to learn to walk, while a kitten 
or a puppy has no such difficulty? 

17. Explain why the use of a cane by old people makes it easier 
for them to walk? 

(6) Falling Bodies 

94. Falling Bodies. One of the earliest physical facts 
learned by a child is that a body unsupported falls toward 
the earth. When a child lets go of a toy, he soon learns to 
look for it on the floor. It is also of common observation 
that light objects, as feathers and paper, fall much slower 
than a stone. The information, therefore, that all bodies 



no 



PHYSICS 



actually fall at the same rate in a vacuum or when removed 

from the retarding influence of the air is received with 

surprise. 
This fact may be shown by using what is called a coua 

and feather tube. On exhausting the air from this tube, 
the feather and coin within are seen 
to fall at the same rate. (See Fig. 78.) 
When air is again admitted, the feather 
flutters along behind. 

95. Galileo's Experiment. The fact 
that bodies of different weight tend 
to fall at the same rate was first ex- 
perimentally shown by Galileo by drop- 
ping a 1 -lb. and a 100-lb. ball from the 





Fig. 78. Bodies fall alike 



in a vacuum. 



Fig. 70. Leaning tower 
of Pisa. 



top of the leaning tower of Pisa in Italy (represented in 
Fig. 79). Both starting at the same time struck the 
ground together. Galileo inferred from this that feathers 
and other light objects would fall at the same rate as 
iron or lead were it not for the resistance of the air. After 
the invention of the air pump this supposition was verified 
as just explained. 



FORCE AND MOTION III 

96. Acceleration Due to Gravity. If a body falls freely, 
that is without meeting a resistance or a retarding influ- 
ence, its motion will continually increase. The increase 
in motion is found to be constant or uniform during each 
second. This uniform increase in motion or in velocity 
of a falling body gives one of the best illustrations that 
we have of uniformly accelerated motion. (Art. 75.) On 
the other hand, a body thrown upward has uniformly 
retarded motion, that is, its acceleration is downward. 
The velocity acquired by a falling body in unit time is 
called its acceleration, or the acceleration due to gravity, 
and is equal to 32.16 ft. (980 cm.) per second, downward, 
each second of time. In one second, therefore, a falling 
body gains a velocity of 32.16 ft. (980 cm.) per second, 
downward. In two seconds it gains twice this, and so on. 

In formulas, the acceleration of gravity is represented 
by "g" and the number of seconds by t, therefore the 
formula for finding the velocity, V, 1 of a falling body 
starting from rest is V = gt. In studying gravity (Art. 
89) we learned that its force varies as one moves toward 
or away from the equator. (How?) In latitude 3 8 the 
acceleration of gravity is 980 cm. per second each second 
of time. 

97. Experimental Study of Falling Bodies. To study 
falling bodies experimentally by observing the fall of 
unobstructed bodies is a difficult matter. Many devices 
have been used to reduce the motion so that the action of 
a falling body may be observed within the limits of a 
laboratory or lecture room. The simplest of these, and in 
some respects the most satisfactory, was used by Galileo. 
It consists of an inclined plane which reduces the 
effective component of the force of gravity so that the 
motion of a body rolling down the plane may be observed 

1 V represents the velocity of a falling body at the end of / seconds. 



112 



PHYSICS 



for several seconds. For illustrating this principle a steel 
piano wire has been selected as being the simplest and the 
most easily understood. This wire is stretched taut across 
a room by a turn-buckle so that its slope is about one in 
sixteen. (See Fig. 80.) Down this wire a weighted pul- 
ley is allowed to run and the distance it travels in 1, 2,3, 
and 4 seconds is observed. From these observations we 
can compute the distance covered each second and the 
velocity at the end of each second. 




Fig. 80. Apparatus to illustrate uniformly accelerated motion. 

In Fig. 63, if OG represents the weight of the body or 
the pull of gravity, then the line OR will represent the 
effective component along the wire, and OS the non-effect- 
ive component against the wire. Since the ratio of the 
height of the plane to its length is as one to sixteen, then 
the motion along the wire in Fig. 80 will be one-sixteenth 
that of a falling body. 

98. Summary of Results. The following table gives 
the results that have been obtained with an apparatus 
arranged as shown above. 

In this table, column 2 is the one which contains the 
results directly observed by the use of the apparatus. Col- 
umns, 3, 4, and 5 are computed from preceding columns. 



FORCE AND MOTION 



"3 



(1) 


(2) 


(3) 


(4) 


(S) 


No. of 


Total dis- 


Distance 


Velocity at 


Acceleration 


seconds 


tance moved 


each second 


end of second 


each second 




- 




Per second 


Per second 


1 


30 cm. 


30 cm. 


60 cm. 


60 cm. 


2 


120 cm. 


90 cm. 


120 cm. 


60 cm. 


3 


270 cm. 


150 cm. 


180 cm. 


60 cm. 


4 


480 cm. 


210 cm. 


240 cm. 


60 cm. 



Column 5 shows that the acceleration is uniform, or the 
same each second. Column 4 shows that the velocity 
increases with the number of seconds or that V = at. Col- 
umn 3 shows that the increase in motion from 1 second 
to the next is just equal to the acceleration or 60 cm. This 
is represented by the following formula : s = % a(2t 1). 

The results of the second column, it may be seen, in- 
crease as 1:4:9:16, while the number of seconds vary as 
1:2:3:4. That is, the total distance covered is proportional 
to the square of the number of seconds. 

This fact expressed as a formula gives: S= \ at 2 . 

Substituting g, the symbol for the acceleration of 
gravity, for a in the above formulas, we have: 
(1) V = gt, (2) S=hgt\ (3) * = U(2/-i). 

99. Laws of Falling Bodies. These formulas may be 
stated as follows for a body which falls from rest: 

1. The velocity of a freely falling body at the end of any 
second is equal to 32.16 ft. per sec. or 980 cm. per second 
multiplied by the number of the second. 

2. The distance passed through by a freely falling body 
during any number of seconds is equal to the square of the 
number of seconds multiplied by 16.08 ft. or 490 cm. 

3. The distance passed through by a freely falling body 
during any second is equal to 16.08 feet or 490 cm. multi- 
plied by one less than twice the number of the second. 



114 PHYSICS 

Important Topics 
i. Falling bodies. 

2. Galileo's experiment. 

3. Acceleration due to gravity. 

4. Laws of falling bodies. 

Exercises 

1. How far does a body fall during the first second? Account for 
the fact that this distance is numerically equal to half the 
acceleration. 

2. (a) What is the velocity of a falling body at the end of the first 
second? (b) How far does it fall during the second second? 
(c) Account for the difference between these numbers. 

3. What is the velocity of a falling body at the end of the fifth 
second? 

4. How far does a body fall (a) in 5 seconds (b) in 6 seconds (c) 
during the sixth second? 

5. (a) What is the difference between the average' velocity during 
the sixth second and the velocity at the beginning of that 
second ? 

(b) Is this difference equal to that found in the second problem ? 
Why? 

6. A stone dropped from a cliff strikes the foot of it in 5 seconds. 
What is the height of the cliff? 

7. Why is it that the increased weight of a body when taken 
to higher latitudes causes it to fall faster, while at the same 
place a heavy body falls no faster than a fight one? 

8. When a train is leaving a station its acceleration gradually 
decreases to zero, although the engine continues to pull. 
Explain. 

9. Would you expect the motion of equally smooth and perfect 
spheres of different weight and material to be equally accel- 
erated on the same inclined plane ? Give reason for your answer. 
Try the experiment. 

10. A body is thrown upward with the velocity of 64.32 ft. per sec. 
How many seconds will it rise? How far will it rise? How 
many seconds will it stay in the air before striking the ground? 

11. 32.16 feet = how many centimeters? 

12. The acceleration of a freely falling body is constant at any 
one place. What does this show about the pull which the 
earth exerts on the body? 



FORCE AND MOTION 



US 



/ 



/ 



\ 



\ 



(7) The Pendulum 

100. The Simple Pendulum. Any body suspended so 
as to swing freely to and fro is a pendulum, as in Fig. 81. 
A simple pendulum is defined as a single particle of matter 
suspended by a cord without weight. It is of course im- 
possible to construct such a pendulum. A small metal 
ball suspended by a thread * 

is approximately a simple 
pendulum. When allowed to 
swing its vibrations are made 
in equal times. This feature 
of the motion of a pendulum 
was first noticed by Galileo 
while watching the slow 
oscillations of a bronze 
chandelier suspended in the 
Cathedral in Pisa. 

10 1. Definition of Terms. 
The center of suspension is 
the point about which the 
pendulum swings. A single 
vibration is one swing across the arc. A complete or double 
vibration is the swing across the arc and back again. The 
time required for a double vibration is called the period. 
The length of a simple pendulum is approximately the dis- 
tance from the point of support to the center of the bob. 

A seconds pendulum is one making a single vibration 
per second. Its length at sea-level, at New York is 
99.31 cm. or 39.1 in., at the equator 39.01 in., at the poles 
39.22 in. 

A compound pendulum is one having an appreciable por- 
tion of its mass elsewhere than in the small compact 
body or sphere called a bob. The ordinary clock pendu- 



\ 
\ 
\ 

i. 

^c 



D 



Fig. 81. A simple pendulum. 



Il6 PHYSICS 

lum or a meter stick suspended by one end are examples 
of compound pendulums. 

The amplitude of a vibration is one-half the arc through 
which it swings, for example, the arc DC or the angle DAC 
in Fig. 81. 

102. Laws of the Pendulum. The following laws may- 
be stated: 

i. The period of a pendulum is not affected by its 
mass or the material of which the pendulum is made. 

2. For small amplitudes, the period is not affected by 
the length of the arc through which it swings. 

3. The period is directly proportional to the square root 

t VI 
of the length. Expressed mathematically, -, = t=- 

103. Uses of the Pendulum. The chief use of the pen- 
dulum is to regulate motion in clocks. The wheels are 
kept in motion by a spring or a weight and the regulation 
is effected by an escapement (Fig. 82). At each vibration 
of the pendulum one tooth of the wheel D slips past the 
prong at one end of the escapement C, at the same time 
giving a slight push to the escapement. This push trans- 
mitted to the pendulum keeps it in motion. In this way, 
the motion of the wheel work and the hands is controlled. 
Another use of the pendulum is in finding the acceleration 

of gravity, by using the formula, / = tc\\-> in which / is 

the time in seconds of a single vibration and I the length 
of the pendulum. If, for example, the length of the 

seconds pendulum is 99.31 cm., then 1 = t\\ ', squaring 

v t 

. 99'3 I 
both sides of the equation, we have i 2 = t 2 , or g = 

o 
2 \s 

jp^ = 980.1 cm. per sec, per sec. From this it fol- 



FORCE AND MOTION 



117 



lows that, since the force of gravity depends upon the 
distance from the center of the earth, the pendulum may 
be used to determine the elevation of a place above sea 
level and also the shape of the earth. 



Important Topics 

1. Simple pendulum. 

2. Definitions of terms used. 

3. Laws of the pendulum. 

4. Uses of the pendulum. 

Exercises . 

1. What is the usual shape of the bob of a 
clock pendulum ? Why is this shape used 
instead of a sphere? 

2. Removing the bob from a clock pendulum 
has what effect on its motion? Also on 
the motion of the hands? 

3. How does the expansion of the rod of a 
pendulum in summer and its contraction 
in winter affect the keeping of time by a 
clock? How can this be corrected? 

4. Master clocks that control the time of a 
railway system have a cup of mercury for 
a bob. This automatically keeps the 
same rate of vibration through any 
changes of temperature. How? 

5. How will the length of a seconds pendu- 
lum at Denver, 1 mile above sea-level, 
compare with one at New York? Why? 

6. What is the period of a pendulum 9 in. long? Nole. In 
problems involving the use of the third law, use the length of a 
seconds pendulum for /, and call its period 1. 

7. A swing is 20 ft. high, find the time required for one swing across 
the arc. 

8. A pendulum is 60 cm. long. What is its period? 

9. If in a gymnasium a pupil takes 3 sec. to swing once across 
while hanging from a ring, how long a pendulum is formed? 

10. A clock pendulum makes four vibrations a second, what is its 
length? 




Fig. 82. Escape- 
ment and pendulum 
of a clock. 



Il8 PHYSICS, 

Review Outline : Force and Motion 

Force; definition, elements, how measured, units, dyne. 

Graphic Representation; typical examples of finding a component, 

a resultant, or an equilibrant. 
Motion; Laws of motion (3), inertia, curvilinear motion, centrifugal 

force, momentum, (M = mv), reaction, stress and strain. 
Moment of Force; parallel forces, couple, effective and non-effective 

component. 
Gravitation; law; gravity, center of; weight. Equilibrium 3 forms; 

stability, how increased. 
Falling Bodies; velocity, acceleration, " g,"Laws; V = gl, S =Hgt 2 

- s = Hg(2t - 1). ' 

Pendulum; simple, seconds, laws (3), t = irVl/g. 



CHAPTER VI 
WORK AND ENERGY 

104. Work. "Whenever a force moves a body upon 
which it acts, it is said to do work upon that body." For 
example, if a man pushes a wheelbarrow along a path, he 
is doing work on it as long as the wheelbarrow moves, but 
if the wheelbarrow strikes a stone and the man continues 
to push and no motion results, from a scientific point of 
view he is then doing no work on it. 

"Work signifies the overcoming of resistance," and 
unless the resistance is overcome no work is done. Lifting 
a weight is doing work on it, supporting a weight is not, al- 
though the latter may be nearly as tiresome as the former. 
Work as used in science is a technical term. Do not 
attach to it meanings which it has in everyday speech. 

105. Measurement of Work. Work is measured by the 
product of the force by the displacement caused in the 
direction of the force, that is W = fs. Therefore if a 
unit of force acts through a unit of space, a unit of work 
will be done. There are naturally several units of work 
depending upon the units of force and space employed. 

English Work Unit. If the force of one pound acts 
through the distance of one foot, a foot-pound of work is 
done. A foot-pound is defined as the work done when 1 
lb. is lifted 1 ft. against the force of gravity. 

Metric Work Unit. If the force is one kilogram and 
the distance one meter, one kilogram-meter of work is done. 

Absolute Work Unit. If the force of one dyne acts 
through the distance of one centimeter a dyne-centimeter 

119 



1 20 PHYSICS 

of work is done. This usually is called an erg. Other 
work units are sometimes used depending upon the force 
and distance units employed. One, the joule, is equal to 
10,000,000 ergs or io 7 ergs. 

Problem. If a load is drawn 2 miles by a team exerting 500 
lbs. force, how much work is done? 

Solution. Since the force employed is 500 lbs., and the dis- 
tance is 2 X 5280 ft., the work done is 500 X 2 X 5280 or 5,280,000 
ft .-lbs. 

106. Energy. In the various cases suggested in the 
paragraphs. upon work, an agent, a man, an animal or a 
machine, was mentioned as putting forth an effort in order 
to do the work. It is also true that in order to perform 
work an agent must employ energy, or the energy of a body 
is its capacity J or doing work. Where an agent does work 
upon a body, as in winding up a spring or in lifting a weight, 
the body upon which the work has been done may acquire 
energy by having work done upon it. That is, it may 
become able to do work itself upon some other body. 
For instance, a lifted weight in falling back to its first 
position may turn wheels, or drive a post into the ground 
against resistance; a coiled spring may run clock work, 
strike a blow, or close a door. Hence the energy, or the 
capacity for doing work, is often acquired by a body 
because work has first been done upon that body. 

107. Potential Energy. The wound up spring may do 
work because work has first been done upon it. The lifted 
weight may also do work because work has first been done 
in raising it to its elevated position since in falling it may 
grind an object to powder, lift another weight or do some 
other kind of work. The energy that a body possesses on 
account of its position or shape and a stres s to which it is 
subjected is called potential energy. The potential energy 
of a body is measured by the work done in lifting it, 



WORK AND ENERGY 121 

changing its shape, or by bringing about the conditions 
by which it can do work. Thus if a block of iron weigh- 
ing 2000 lbs. is lifted 20 ft., it possesses 40,000 ft.-lbs. of 
potential energy. It is therefore able to do 40,000 ft.-lbs. 
of work in falling back to its first position. If the block 
just mentioned should tall from its elevated position upon 
a post, it could drive the post into the ground because its 
motion at the instant of striking enables it to do work. To 
compute potential energy you compute the work done upon 
the body. That is, P.E. = w X h or/ X s. 

108. Kinetic Energy. The energy due to the motion 
of a body is called kinetic energy. The amount of kinetic 
energy in a body may be measured by the amount ot work 
done to put it in motion. It is usually computed, how- 
ever, by using its mass and velocity on striking. To illus- 
trate, a 100-lb. ball is lifted 16 ft. The work done upon 
it, and hence its potential energy, is 1600 ft.-lbs. On fall- 
ing to the ground again, this will be changed into kinetic 
energy, or there will be 1600 ft.-lbs. of kinetic energy on 
striking. It will be noted that since energy is measured 
by the work it can do, work units are always used in meas- 
uring energy. To compute the kinetic energy of a falling 
body by simply using its mass and velocity one proceeds 
as follows, in solving the above problem: 

First, find the velocity of the falling body which has fallen 16 

ft. A body falls 16 ft. in one second. In this time it gains a velocity 

of 32 ft. per second. Now using the formula for kinetic energy 

wv 2 100X32X32 -\ -. . , 

K.E. , we have K.E.= =1000 ft.-lbs. as before. 

2g 2X32 

WV 2 

The formula, K.E. = -x- , may be derived in the following 

manner: 

The kinetic energy of a falling body equals the work done in giv- 
ing it its motion, that is, K.E. = w X S, in which, w = the weight 
of the body and 5 = the distance the body must fall freely in order 



12 2 HYSICS 

to acquire its velocity. The distance fallen by a freely falling body, 

S, = Hgt* = y~ ( Art - o8 P- IIX )- Now > v = # and v * = s** 2 - 

Substituting for gH z , its equal v 2 , we have S = 3-. Substituting 

this value of 5 in the equation K.E. = w X S, we have ... 

= w 

Since the kinetic energy of a moving body depends upon its mass 
and velocity and not upon the direction of motion, this formula may 
be used to find the kinetic energy of any moving body. Mass and 
weight in such problems may be considered numerically equal. 

Important Topics 
i. Work defined. 

2. Work units, foot-pound, kilogram-meter, erg. 

3. Energy defined. 

4. Kinds of energy, potential and kinetic. 

Problems 

1. How much work will a 120-lb. boy do climbing a mountain 3000 
ft. high? Should the vertical or slant height be used? Why? 

2. In a mine 4000 kg. of coal are lifted 223 meters: how much work 
is done upon the coal? What is the kind and amount of energy 
possessed by the coal? 

3. A pile driver weighs 450 lbs. It is lifted 16 ft. How much work 
has been done upon it? What kind and amount of energy will 
it have after falling 16 ft. to the pile? 

4. A train weighing 400 tons is moving 30 miles per hour. Com- 
pute its kinetic energy. (Change its weight to pounds and 
velocity to feet per second.) 

5. What would be the kinetic energy of the train in problem 4 if it 
were going 60 miles per hour? If it were going 90 miles per 
hour? How does doubling or trebling the speed of an object 
affect its kinetic energy? How does it affect its momentum? 

6. What is the kinetic energy of a 1600-lb. cannon ball moving 
2000 ft. per second? 

7. Mention as many kinds of mechanical work as you can and show 
how each satisfies the definition of work. 

8. A pile driver weighing 3000 lbs. is lifted 10 ft. How much work 
is done upon it? 



WORK AND ENERGY 1 23 

9. If the pile driver in problem 8 is dropped upon the head of a 
pile which meets an average resistance of 30,000 lbs., how far 
will one blow drive it? 
10. A 40 kg. stone is placed upon the top of a chimney 50 meters 
high. Compute the work done in kilogram-meters and foot- 
pounds. 

(2) Power and Energy 

109. Horse-power. In computing work, no account 
is taken of the time required to accomplish it. But since 
the time needed to perform an undertaking is of much 
importance, the rate of work, or the power or activity of 
an agent is an important factor. Thus if one machine 
can do a piece of work in one-fifth the time required by 
another machine, it is said to have five times the power of 
the other. Therefore the power of a machine is the rate 
at which it can do work. James Watt (1736-18 19), the 
inventor of the steam-engine, in expressing the power of 
his engine, used as a unit a horse-power. He considered 
that a horse could do 33,000 ft.-lbs. of work a minute. 
This is equal to 550 ft.-lbs. per second or 76.05 kg.-m. per 
second. This is too high a value but it has been used ever 
since his time. Steam engines usually have their power 
rated in horse-power. That is, locomotives produce from 
500 to 1500 horse-power. Some stationary and marine 
engines develop as high as 25,000 horse-power. The 
power of an average horse is about % horse-power and of a 
man about % horse-power when working continuously 
for several hours. 

no. The Watt. In the metric system, the erg as a 
unit of work would give as a unit of power 1 erg per second. 
This amount is so small, however, that a larger unit is 
usually employed, the practical unit being 10,000,000 ergs 
a second, that is, one joule per second. (See Art. 105.) 
This practical unit is called a Watt after James Watt. 



124 PHYSICS 

The power of dynamos is usually expressed in kilowatts, 
a kilowatt representing iooo watts. Steam-engines in 
modern practice are often rated in kilowatts instead of 
horse-power. A horse-power is equivalent to 746 watts, 
or is nearly 3/4 of a kilowatt. 

in. Energy. Its Transference and Transformation. 
We have considered energy as the capacity for doing work, 
and noted the two kinds, potential and kinetic, and the 
facility with which one may change into another. In 
fact, the transference of energy from one body to another, 
and its transformation from one form to another is one 
of the most common processes in nature. Take a pendu- 
lum in motion, at the end of a swing, its energy being 
entirely due to its elevated position is all potential; at the 
lowest point in its path its energy being entirely due to its 
motion is all kinetic. The change goes on automatically 
as long as the pendulum swings. A motor attached by a 
belt to a washing machine is started running. The energy 
of the motor is transferred by the belt to the washer where 
it is used in rubbing and moving the clothes. 

The heat used in warming a house is usually obtained 
by burning coal or wood. Coal is believed to be formed 
from the remains of plants that grew in former geologic 
times. These plants grew through the help of the radiant 
energy of the sun. The following are transformations 
of energy that have occurred: The radiant energy of 
sunlight was transformed into the chemical energy of the 
plants. This remained as chemical energy while the 
plants were being converted into coal, was mined, brought 
to the stove or furnace and burned. The burning trans- 
formed the chemical energy into heat energy in which form 
we use it for warming rooms. Take the energy used in 
running a street car whose electrical energy comes from a 
waterfall. The energy of the car itself is mechanical. 



WORK AND ENERGY I 25 

Its motor, however, receives electrical energy and trans- 
forms it into mechanical. This electrical energy comes 
along a wire from a dynamo at the waterfall, where water- 
wheels and generators transform into electrical energy the 
mechanical energy of the falling water. The water 
obtained its energy of position by being evaporated by 
the heat of the radiant energy of the sun. The vapor 
rising into the air is condensed into clouds and rain, and 
falling on the mountain side, has, from its elevated posi- 
tion, potential energy. The order of transformation, 
therefore, is in this case, radiant, heat, mechanical, electri- 
aal, and mechanical. Can you trace the energy from 
the sun step by step to the energy you are using in reading 
this page? 

112. Forms of Energy. A steam-engine attached to a 
train of cars employs its energy in setting the cars in 
motion, i.e., in giving them kinetic energy and in over- 
coming resistance to motion. But what is the source of 
the energy of the engine? It is found in the coal which it 
carries in its tender. But of what kind? Surely not 
kinetic, as no motion is seen. It is therefore potential. 
What is the source of the energy of the coal? This ques- 
tion leads us back to the time of the formation of coal beds, 
when plants grew in the sunlight and stored up the energy 
of the sun's heat and light as chemical energy. The 
sun's light brings to the earth the energy of the sun, 
that central storehouse of energy, which has supplied 
nearly all the available energy upon the earth. Five 
forms of energy are known, viz., mechanical, heat, elec- 
trical, radiant, and chemical. 

113. Energy Recognized by its Effects. Like force, 
energy is invisible and we are aware of the forms only by 
the effects produced by it. 

We recognize heat by warming, by expansion, by 
pressure. 



126 PHYSICS 

We recognize light by warming, by its affecting 
vision. 

We recognize electrical energy by its heat, light, motion, 
or magnetic effect. We recognize mechanical energy by 
the motion that it produces. We recognize chemical energy 
by knowing that the source of energy does not belong to 
any of the foregoing. 

A boy or girl is able to do considerable work. They 
therefore possess energy. In what form does the energy 
of the body mainly occur? One can determine this for 
himself by applying questions to each form of energy in 
turn as in Art. 114. 

114. Source of the Energy of the Human Body. Is 
the energy of the human body mostly heat? No, since we 
are not very warm. Is it light or electrical? Evidently 
not since we are neither luminous nor electrical. Is it 
mechanical? No, since we have our energy even when 
at rest. Is it chemical? It must be since it is none 
of the others. Chemical energy is contained within the 
molecule. 

It is a form of potential energy and it is believed to be 
due to the position of the atoms within the molecule. As a 
tightly coiled watch spring may have much energy within 
it, which is set free on allowing the spring to uncoil, so 
the chemical energy is released on starting the chemical 
reaction. Gunpowder and dynamite are examples of 
substances containing chemical energy. On exploding 
these, heat, light, and motion are produced. Gasoline, 
kerosene, and illuminating gas are purchased because of 
the potential energy they contain. This energy is set 
free by burning or exploding them. 

The source of the energy of our bodies is of course the 
food we eat. The energy contained in the food is also 
cjiemical. Vegetables obtain their energy from the sun- 



WORK AND ENERGY 1 27 

light (radiant energy) . This is why plants will not grow 
in the dark. The available energy is mostly contained in 
the form of starch, sugar and oil. Digestion is employed 
principally to dissolve these substances so that the blood 
may absorb them and carry them to the tissues of the body 
where they are needed. The energy is set free by oxida- 
tion (burning), the oxygen needed for this being supplied 
by breathing. Breathing also removes the carbon diox- 
ide, which results from the combustion. It is for its 
energy that our food is mostly required. 

115. Conservation of Energy. In the study of matter 
we learned that it is indestructible. Energy is also 
believed to be indestructible. This principle stated con- 
cisely teaches that despite the innumerable changes which 
energy undergoes the amount in the universe is unchange- 
able, and while energy may leave the earth and be lost 
as far as we are concerned, that it exists somewhere in 
some form. The principle which teaches this is called the 
" Conservation of Energy." The form into which energy 
is finally transformed is believed to be heat. 

Important Topics 

1. Power denned. Units. Horse-power. Watt. 

2. Transference and transformations of energy. 

3. Forms of energy; heat, electrical, mechanical, radiant, chemical. 

4. Effects of the several forms of energy. 

5. Energy of the human body. 

6. Conservation of energy. 

Exercises 

1. A boy weighing no lbs. ran up a stairs 10 ft. high, in 4 sec- 
onds. How much work was done? What was his rate of 
work (foot-pounds per second)? Express also in horse-power. 

2. A locomotive drawing a train exerts a draw bar pull of 11,000 
lbs. How much work does it do in moving 3 miles? What 



128 PHYSICS 

is its rate of work if it moves 3 miles in 5 minutes? Express in 
horse-power. 1 

3. If 400 kg. are lifted 35 meters in 5 seconds what work is done? 
What is the rate of work? Express in horse-power, watts and 
kilowatts. 

4. Trace the energy of a moving railway train back to its source in 
the sun. 

5. Why does turning the propeller of a motor boat cause the boat 
to move? 

6. Does it require more power to go up a flight of stairs in 5 
seconds than in 10 seconds? Explain. Is more work done in 
one case than in the other? Why? 

7. Can 1 man carrying bricks up to a certain elevation for 120 
days do as much work as 120 men carrying up bricks for 1 day? 

8. If the 1 man and 1 20 men of problem 7 do the same amount of 
work have they the same power? Explain. 

9. If 160 cu. ft. of water flow each second over a dam 15 ft. high 
what is the available power? 

10. What power must an engine have to fill a tank 11 X 8 X 5 ft. 
with water 120 ft. above the supply, in 5 minutes? 

11. A hod carrier weighing 150 lbs. carries a load of bricks weighing 
100 lbs. up a ladder 30 ft. high. How much work does he do? 

12. How much work can a 4-horse-power engine do in 5. minutes? 

13. Find the horse-power of a windmill that pumps 6 tons of water 
from a well 90 ft. deep in 30 minutes. 

14. How many horse-power are there in a waterfall 20 ft. high over 
which 500 cu. ft. of water pass in a minute? 

15. The Chicago drainage canal has a flow of about 6000 cu. ft. a 
second. If at the controlling works there is an available fall of 
34 ft. how many horse-power can be developed? 

16. How long will it take a 10-horse-power pump to fill a tank 
of 4000 gallons capacity, standing 300 ft. above the pump? 

17. A boy weighing 162 lbs. climbs a stairway a vertical height of 
14 ft. in 14.6 seconds. How much power does he exert? 

18. The same boy does the same work a second time in 4.2 seconds. 
How much power does he exert this time? What causes the 
difference? 

19. What is a horse-power-hour? a kilowatt-hour? 

1 The following formula is of assistance in computing horse-power in 

,, lbs. X ft. 

problems: H. p. = rz ' 

55 X sec. 



work and energy 120, 

(3) Simple Machines and the Lever 

116. Machines and Their Uses. A man, while stand- 
ing on the ground, can draw a flag to the top of a pole, 
by using a rope passing over a pulley. 

A boy can unscrew a tightly fitting nut that he cannot 
move with his fingers, by using a wrench. 

A woman can sew a long seam by using a sewing ma- 
chine in much less time than by hand. 

A girl can button her shoes much quicker and easier 
with a button-hook than with her fingers. 

These illustrations show some of the reasons why 
machines are used. In fact it is almost impossible to do 
any kind of work efficiently without using one or more 
machines. 

117. Advantages of Machines. (a) Many machines 
make possible an increased speed as in a sewing machine 
or a bicycle. 

(b) Other machines exert an increased force. A rope 
and a set of pulleys may enable a 
man to lift a heavy object such as 
a safe or a piano. By the use of 
a bar a man can more easily move 
a large rock. (See Fig. 83.) Fig. 83 The rock is easily 

(c) The direction of a force 

may be changed thus enabling work to be done that 
could not be readily accomplished otherwise. As, e.g., 
the use of a pulley in raising a flag to the top of a flag pole, 
or in raising a bucket of ore from a mine by using a horse 
attached to a rope passing over two or more pulleys. 
(See Fig. 84.) 

(d) Other agents than man or animals can be used such as 
electricity, water power, the wind, steam, etc. Fig. 85 
represents a windmill often used in pumping water. 




130 



PHYSICS 



A machine is a device for transferring or transforming en- 
ergy. It is usually therefore an instrument for doing work. 
An electric motor is a machine since it transforms the 
energy of the electric current into motion or mechanical 
energy, and transfers the energy from the wire to the 
driving pulley. 

118. A Machine Cannot Create Energy. Whatever 
does work upon a machine (a man, moving water, wind, 
etc.) loses energy which is employed in doing the work of the 




Fig. 84. The horse lifts the bucket of ore. 



machine. A pair of shears is a machine since it transfers 
energy from the hand to the edges that do the cutting. 
Our own bodies are often considered as machines since 
they both transfer and transform energy. 

We must keep in mind that a machine cannot create 
energy. The principle of "Conservation of Energy" 
is just as explicit on one side as the other. Just as energy, 
cannot be destroyed, so energy cannot be created. A 
machine can give out no more energy than is given to it. 
It acts simply as an agent in transferring energy from one 



WORK AND ENERGY 



131 



body to another. Many efforts have been made to con- 
struct machines that when once started will run themselves, 
giving out more energy than they receive. Such efforts, 
called seeking for perpetual motion, have never succeeded. 
This fact is strong evidence in 
favor of the principle of the con- 
servation of energy. 

119. Law of Machines. 
When a body receives energy, 
work is done upon it. There- 
fore work is done upon a 
machine when it receives en 1 
ergy and the machine does 
work upon the body to which it 
gives the energy. In the oper- 
ation of a machine, therefore, 
two quantities of work are to 
be considered and by the prin- 
ciple of the conservation of 
energy, these , two must be 
equal. The work done by a 
machine equals the work done 
upon it, or the energy given out 
by a machine equals the energy 
received by it. These two 

quantities of work must each be composed of a force 
factor and a space factor. Therefore two forces and 
two spaces are to be considered in the operation of a 
machine. The force factor of the work done on the 
machine is called the force or effort. It is the force applied 
to the machine. The force factor of the work done by a 
machine is called the weight or resistance. It is the force 
exerted by the machine in overcoming the resistance and 
equals the resistance overcome. 




Fig. 85. A windmill. 



132 PHYSICS 

If/ represents the force or effort, and D f the space it acts 
through, and w represents the weight or resistance, and 
D w the space it acts through, then the law of machines 
may be expressed by an equation, / X D f = w X D w . 
That is, the effort times the distance the effort acts equals the 
resistance times the distance the resistance is moved or over- 
come. When the product of two numbers equals the 
product of two other numbers either pair may be made 
the means and the other the extremes of a proportion. 
The equation given above may therefore be expressed 
w :f= D f :D w . Or the resistance is to the effort as the 
effort distance is to the resistance distance. The law of 
machines may therefore be expressed in several ways. 
One should keep in mind, however, that the same law of 
machines is expresed even though the form be different. 
What two ways of expressing the law are given? 

120. The Simple Machines. There are but six simple 
machines. All the varieties of machines known are 
simply modifications and combinations of the six simple 
machines. The six simple machines are more easily 
remembered if we separate them into two groups of three 
each. The first or lever group consists of those machines 
in which a part revolves about a fixed axis. It contains 
the lever, pulley and wheel and axle. The second or in- 
clined plane group includes those having a sloping surface. 
It contains the inclined plane, the wedge, and the screw. 

121. The Lever. The lever is one of the simple ma- 
chines most frequently used, being seen in scissors, broom, 
coal shovel, whip, wheelbarrow, tongs, etc. The lever 
consists of a rigid bar capable of turning about a fixed axis 
called the fulcrum. In studying a lever, one wishes to 
know what weight or resistance it can overcome when a 
certain force is applied to it. Diagrams of levers, there- 
fore, contain the letters w and /. In addition to these, O 



WORK AND ENERGY 



*33 



stands for the fulcrum on which it turns. By referring 
to Fig. 86, a, b, c, one may notice that each of these may 
occupy the middle position between the other two. The 
two forces (other than the one exerted by the fulcrum) 
acting on a lever always oppose each other in the matter 
of changing rotation. They may be considered as a 
pair of parallel forces acting on a body, each tending to 
produce rotation. 

a b s c 

j/jj ]F_ 



IVk 




The three classes of levers. 



122. Moment of Force. The effectiveness of each force 
may therefore be determined by computing its moment 
about the fixed axis (see Art. 84), that is, by multiplying 
each force by its distance to the fulcrum or axis of rota- 
tion. Let a meter stick have a small hole bored through 
it at the 50 cm. mark near one edge, and let it be mounted 
on a nail driven into a vertical support and balanced by 
sliding a bent wire along it. Suspend by a fine wire or 
thread a 100 g. weight, 15 cm. from the nail and a 50 g. 
weight 30 cm. from the nail, on the other side of the sup- 
port. These two weights will be found to balance. When 
viewed from this side A (Fig. 87) tends to turn the lever 
in a clockwise direction (down at right), B in the counter- 
clockwise direction (down at left). Since the lever bal- 
ances, the forces have equal and opposite effects in changing 
its rotation as may also be computed by determining the 



134 PHYSICS 

moment of each force by multiplying each by its dis- 
tance from the fulcrum. Therefore the effectiveness of a 
force in changing rotation depends upon the distance from 
it to the axis as well as upon the magnitude of the force. 

lo o From the experi- 

' ment just described, 

the moment of the 

acting force equals 

the moment of the 



I I i I I I I I 



\ 12a wei S ht or fXD f = 



Fig. 87. The two moments are equal w X D w , or the effort 
about C. 100 x 15 = so X 30- times the effort arm 

equals the weight times the weight arm. This equation is 
called the law of the lever. It corresponds to the general 
law of machines and may also be written^:/ = D f :D w . 
123. Mechanical Advantage. A lever often gives an 
advantage because by its use one may lift a stone or weight 
which the unaided strength of man could not move. If 
the lever is used in lifting a stone weighing 500 lbs., the 
force available being only 100 lbs., then its mechanical 
advantage would be 5, the ratio oiw.f. In a similar way, 
the mechanical advantage of any machine is found by 
finding the ratio of the resistance or weight to the effort. 
What must be the relative lengths of the effort arm and 
resistance or weight arm in the example just mentioned ? 
Since the effort times the effort arm equals the weight 
times the weight arm, if / X D f = w X D w , then D/ is 
five times D w . Hence the mechanical advantage of a lever 
is easily found by finding the ratio of the effort arm to 
the weight arm. 

Important Topics 

1. Advantage of machines. 

2. Machines cannot create energy. 

3. Law of machines. 



WORK AND ENERGY 



135 



4. Six simple machines. 

5. Lever and principle of moments. 

6. Mechanical advantage of a machine. 

Exercises 

1. Give six examples of levers you use. 

2. Fig. 880 represents a pair of paper shears, S&b a pair of tinner's 




10 



to 

-(d) Paper shears 



(b) 
(b) Tinner's shears. 



6. 



shears. Which has the greater mechanical advantage? Why? 

Explain why each has the most effective shape for its particular 

work. 

Find examples of levers in a sewing machine. 

What would result if, in Art. 122, the 100 g. weight were put 

25 cm. from O and the 50 g. weight 45 

cm. from O? Why? Explain using 

principle of moments. 

How is the lever principle applied in 

rowing a boat? 

When you cut cardboard with shears, 

why do you open them wide and cut 

near the pivot? 

7. In carrying a load on a stick over the 
shoulder should the pack be carried near 
the shoulder or out on the stick? Why? 

8. How can two boys on a see-saw start it 
without touching the ground? 

9. In lifting a shovel full of sand do you 
lift up with one hand as hard as you 
push down with the other? Why? 
Why must the hinges of a gate 3 ft. 
high and 16 ft. wide be stronger than the hinges of a gate 16 

ft. high and 3 ft. wide? 

11. When one sweeps with a broom do the hands do equal amounts 
of work? Explain. 




Fig. 89. The ham- 
mer is a bent lever. 
What is its mechanical 
advantage? 



136 PHYSICS 

12. A bar 6 ft. long is used as a lever to lift a weight of 500 lbs. 
If the fulcrum is placed 6 in. from the weight, what will be 
the effort required? Note: two arrangements of weight, ful- 
crum and effort are possible. 

13. The handle of a hammer is 12 in. long and the claw that is used 
in drawing a nail is 2.5 in. long. (See Fig. 89.) A force of 25 
lbs. is required to draw the nail. What is the resistance of the 
nail? 

14. The effective length of the head of a hammer is 2 in. The 
handle is 15 in. long and the nail holds in the wood with a force 
of 500 lbs. Only 60 lbs. of force is available at the end of the 
handle. What will be the result? 

15. If an effort of 50 lbs. acting on a machine moves 10 ft., how far 
can it lift asweight of 1000 lbs.? 

16. A bar 10 ft. long is to be used as a lever. The weight is kept 
2 ft. from the fulcrum. What different levers can it represent? 

17. The effort arm of a lever is 6 ft., the weight arm & in. How long 
will the lever be? Give all possible answers. 

18. Two boys carry a weight of 100 lbs. on a pole 5 ft. long between 
them. Where should the weight be placed in order that one boy 
may carry one and one-fourth times as much as the other? 

(4) The Wheel and Axle and the Pulley 

124. The Wheel and Axle. 1. One of the simple ma- 
chines most commonly applied in compound machines is 
the wheel and axle. It consists of a wheel H mounted 
on a cylinder Y so fastened together that both turn on 
the same axis. In Fig. 90, ropes are shown attached to 
the circumferences of the wheel and axle. Sometimes a 
hand wheel is used as on the brake of a freight or street 
car, or simply a crank and handle is used, as in Fig. 91. 
The capstan is used in moving buildings. Sometimes 
two or three wheels and axles are geared together as on a 
derrick or cr ane as in Fig. 92. 

Fig. 93 is a diagram showing that the wheel and axle 
acts like a lever. The axis D is the fulcrum, the effort 
is applied at F, at the extremity of a radius of the wheel 



WORK AND ENERGY 



137 




Fig. 90. The wheel and axle 




Fig. 91. Windlass used in draw- 
ing water from a well. 





HE\ 



Fig. 92. A portable crane. 



Fig . 93 . The wheel and axle 
considered as a lever. 



138 



PHYSICS 



and the resisting weight W at the extremity of a radius 
of the axle. Hence, if D f , the effort distance, is three 



1 

4 


2 JjL 


3 




4 


r5? 






















& .**; 






5- 


I i T"" 
















c.o 
sum 


Q 


fcj 


E^^ 


1 ~ ~^ii r" 




v8 


mmm . ff -^^^ ' "n/cj 




hll=5^i ^<L 
















'.Q<^ 






7 










Fig. 94. View of transmission gears in an automobile. 1, Drive gear; 
2, High and intermediate gear; 3, Low and reverse gear; 4, 8, Reverse 
idler gears; 5, 6, 7, Countershaft gears. (Courtesy of the Automobile 
Journal.) 




Fig. 95. Reducing gear of a steam turbine. 

times D w , the weight distance, the weight that can be 
supported is three times the effort. Here as in the lever, 



WORK AND ENERGY I39 

/ X Df = w X D w , or w:f = D f :D w , or the ratio of the 
weight to the effort equals the ratio of the radius of the wheel 
to the radius of the axle. This is therefore the mechanical 
advantage of the wheel and axle. Since the diameters 
or circumferences are in the same ratio as the radii these 
can be used instead of the radii. Sometimes, when 
increased speed instead of increased force is desired, the 
radius of the wheel or part to which power is applied is 
less than that of the axle. This is seen in the bicycle, 
buzzsaw, and blower. Sometimes geared wheels using the 
principle of the wheel and axle are used to reduce speed, 
as in the transmission of an automobile (see Fig. 94), or the 
reducing gear of a steam turbine. (See Figs. 95 and 293.) 

A bevel gear is frequently used to change the direction 
of the force. (See Fig. 94.) 

125. The Pulley. The pulley consists of a wheel turn- 
ing on an axis in a frame. The wheel is called a sheave and 
the frame a block. The rim may be smooth or grooved. 
The grooved rim is used to hold a cord or rope. One use of 
the pulley is to change the direction of the acting force as 
in Fig. 84, where pulley B changes a horizontal pull at H 
to a downward force and pulley A changes this into an 
upward force lifting the weight W. These pulleys are fixed 
and simply change the direction. Without considering 
the loss by friction, the pull at W will equal that at F. 
Sometimes, a pulley is attached to the weight and is lifted 
with it. It is then called a movable pulley. In Fig. 96 
the movable pulley is at P, a fixed pulley is at F. When 
fixed pulleys are used, a single cord runs through from the 
weight to the effort, so that if a force of 100 lbs. is applied 
by the effort the same force is received at the weight. But 
with movable pulleys several sections of cord may extend 
upward from the weight each with the force of the effort 
upon it. By this arrangement, a weight several times 
larger than the effort can be lifted. Fig. 97 represents 



140 



PHYSICS 



what is called a block and tackle. If a force of 50 lbs. 
is exerted at F, each section of the rope will have the same 
tension and hence the six sections of the rope will support 
300 lbs. weight. The mechanical advantage of the pulley 
or the ratio of the weight to the effort, 
therefore, equals the number of sections 
of cord supporting the weight. The 
fixed pulley represents a lever, see 
Fig. 98, where the effort and weight 
are equal. In the movable pulley, 



5 

Fig. 96. A single movable pulley. Fig. 97. Block and tackle. 




W 










D 






Fig. 98. The fixed 
pulley considered as a 



Fig. 99. The mov- 
able pulley considered 
as a lever. 



the fulcrum (see Fig. 99) is at D ; the weight, W, is applied 
at the center of the pulley and the effort atF. The weight 
distance, D w , is the radius, and the effort distance, D f , is 



WORK AND ENERGY 141 

the diameter of the pulley. Since W/F = D f /D w = 2 
in a movable pulley, the weight is twice the effort, or its 
mechanical advantage is 2. 

Important Topics 

1. Wheel and Axle, Law of Wheel and Axle. 

2. Pulley, Fixed and Movable, Block and Tackle, Law of Pulley. 

Exercises 

1. Why do door knobs make it easier to unlatch doors? What 
simple machine do they represent? Explain. 

2. What combination of pulleys will enable a 160-lb. man to raise 
a 900-lb. piano? 

3. When you pull a nail with an ordinary claw hammer, what is 
the effort arm? the resistance arm? 

4. How much work is done by the machine in problem 2 in lifting 
the piano 20 ft. ? How much 

work must be done upon the 
machine to do this work? 

5. The pilot wheel of a boat has 
a diameter of 60 in.; the 
diameter of the axle is 6 in. 
If the resistance is 175 lbs., 
what force must be applied 
to the wheel? 

6. Four men raise an anchor 
weighing ij^ tons, with a 
capstan (see Fig. no) having 
a barrel 9 in. in diameter. Fig. 100. The capstan. 
The circle described by the 

hand-spikes is 13 % ft. in diameter. How much force must 
each man exert? 

7. A bicycle has a 28-in. wheel. The rear sprocket is 3 in. in 
diameter, 1 the radius of the pedal crank is 7 in.; 24 lbs. applied 
to the pedal gives what force on the rim of the wheel? What 
will be the speed of the rim when the pedal makes one revolu- 
tion a second? 

8. Measure the diameters of the large and small pulleys on the 
sewing-machine at your home. What mechanical advantage 

1 Consider the diameter of the front sprocket as 6 inches. 




142 PHYSICS 

in number of revolutions does it give?. Verify your computa- 
tion by turning the wheel and counting the revolutions. 
9. What force is required with a single fixed pulley to raise a 
weight of 200 lbs. ? How far will the effort move in raising the 
weight 10 ft.? What is the mechanical advantage? 

10. In the above problem substitute a single movable pulley for 
the fixed pulley and answer the same questions. 

n. What is the smallest number of pulleys required to lift a weight 
of 600 lbs. with a force of 120 lbs.? How should they be 
arranged? 

12. A derrick in lifting a safe weighing 2 tons uses a system of pulleys 
employing 3 sections of rope. What is the force required? 

13. Name three instances where pulleys are used to do work that 
otherwise would be difficult to do. 

14. Draw a diagram for a set of pulleys by means of which 100 lbs. 
can lift 400 lbs. 

(5) The Inclined Plane. Efficiency 

126. Efficiency. The general law of machines which 
states that the work done by a machine equals the work 
put into it requires a modification, when we apply the law 
in a practical way, for the reason that in using any machine 
there is developed more or less friction due to parts of the 
machine rubbing on each other and to the resistance of the 
air as the parts move through it. Hence the statement of 
the law that accords with actual working conditions runs 
somewhat as follows: The work put into a machine equals 
the useful work done by the machine plus the wasted work 
done by it. The efficiency of a machine is the ratio of the 
useful work done by it to the total work done on the 
machine. If there were no friction or wasted work, the 
efficiency would be perfect, or, as it is usually expressed, 
would be 100 per cent. Consider a system of pulleys into 
which are put 600 ft.-lbs. of work. With 450 ft.-lbs. of 
useful work resulting, the efficiency would be 450 -fc 
600 = %, or 75 per cent. In this case 25 per cent, of the 



WORK AND ENERGY 



143 



work done on the machine is wasted. In a simple lever 
the friction is slight so that nearly 100 per cent, efficiency 
is often secured. 

Some forms of the wheel and axle have high efficiencies 
as in bicycles with gear wheels. Other forms in which 
ropes are employed have more friction. Pulleys have 
sometimes efficiencies as low as 40 per cent, when heavy 
ropes are used. 

127. Inclined Plane. We now come to a type of simple 
machine of lower efficiency than those previously men- 
tioned. These belong to the inclined plane group, which 




Fig. ioi. An inclined plane. 

includes the inclined plane (see Fig. 101), the wedge and 
the screw. They are extensively used, however, notwith- 
standing their low efficiency, on account of often giving a 
high mechanical advantage. The relation between these 
machines may be easily shown, as the wedge is obviously 
a double inclined plane. In Art. 82 it is shown that the 
effort required to hold a weight upon an inclined plane is 
to the weight supported as the height of the plane is to its 
length. 

Or while the weight is being lifted the vertical height 
BC, the effort has to move the length of the plane AC. 
Since by the law of machines the effort times its distance 
equals the weight times its distance, or the weight is to 



144 PHYSICS 

the effort as the effort distance is to the weight distance, 
therefore the mechanical advantage of the inclined plane 
is the ratio of the length to the height of the inclined plane. 
Inclined planes are used to raise heavy objects short 
distances, as barrels into a wagon, and iron safes into a 
building. Stairways are inclined planes with steps cut 
into them. 

128. The Wedge. Wedges are used to separate objects, 
as in splitting wood (see Fig. 102), cutting wood, and where 
great force is to be exerted for short distances. An axe is 
a wedge, so is a knife. A fork consists of several round 

wedges set in a handle. The edge of 
any cutting tool is either an inclined 
plane or a wedge. Our frpnt teeth are 
wedges. Numerous examples of in- 
clined planes may be seen about us. 

No definite statement as to the 
mechanical advantage of the wedge can 
be given as the work done depends 

Fig. 102. One use i arge i y on friction. The force used is 
of the wedge. . 

generally applied by blows on the thick 

end. In general, the longer the wedge for a given thick- 
ness the greater the mechanical advantage. 

129. The Screw. The screw is a cylinder around whose 
circumference winds a spiral groove. (See Fig. 103.) 
The raised part between the two adjacent grooves is the 
thread of the screw. The screw turns in a block called a 
nut, within which is a spiral groove and thread exactly 
corresponding to those of the screw. The distance be- 
tween two consecutive threads measured parallel to the 
axis is called the pitch of the screw. (See Fig. 104.) If 
the thread winds around the cylinder ten times in the 
space of 1 in., the screw is said to have ten threads to the 
inch, the pitch being }{ in. The screw usually is turned 




WORK AND ENERGY 



145 



by a lever or wheel with the effort applied at the end of 
the lever, or at the circumference of the wheel. While the 
effort moves once about the circumference of the wheel the 
weight is pushed forward a distance equal to the distance 
between two threads (the pitch of the screw). The work 
done by the effort therefore equals F X 2-n-r, r being the 
radius of the wheel, and the work done on the weight 
equals W X s, s being the pitch of the screw. By the law 
of machines F X 271T = W X s or W/F 
= 2irr/s. Therefore the mechanical 
advantage of the screw equals 2-n-r/s. 
Since thp distance the weight moves is 
small compared to that the power trav- 
els, there is a great gain in force. The 





Fig. 103. The screw 
is a spiral inclined 
plane. 



Fig. 104. The pitch is 5. 



screw is usually employed where great force is to be exerted 
through small distances as in the vise (Fig. 105) the jack 
screw (Fig. 106), screw clamps, to accurately measure 
small distances as in the micrometer (Fig. 107) and spher- 
ometer, and to lessen the motion in speed-reducing devices. 
The worm gear (Fig. 108) is a modification of the screw 
that is sometimes used where a considerable amount of 
speed reduction is required. 



10 



T46 



PHYSICS 





Fig. 105. A vise. 



Fig 106. A jack 
screw. 




Fig. 107. A micrometer screw. 




Fig. 108. This large worm-wheel is a part of the hoisting mechanism 
employed for the lock gates of the Sault Ste. Marie Canal. 



WORK AND ENERGY 147 



Important Topics 

1. Efficiency of machines. 

2. The inclined plane, wedge and screw. Applications. 

Exercises 

1. A plank 12 ft. long is used to roll a barrel weighing 200 lbs. into 
a wagon 3 ft. high. Find the force required parallel to the 
incline. 

2. How long a plank will be needed to roll an iron safe weighing 1 K 
tons into a wagon 3 ft. high using a pull of 600 lbs. parallel to the 
incline. 

3. An effort of 50 lbs. acting parallel to the plane prevents a 200-lb. 
barrel from rolling down an inclined plane. What is the ratio 
of the length to the height of the plane? 

4. A man can push with a force of 150 lbs. and wishes to raise a box 
weighing 1200 lbs. into a cart 3 ft. high. How long a plank must 
he use? 

5. The radius of the wheel of a letter press is 6 in., the pitch of its 
screw is K in. What pressure is produced by a force of 40 lbs. ? 

6. The pitch of a screw of a vice is % in. the handle is 1 ft. long. 
What pressure can be expected if the force used is 100 lbs.? 

7. A jackscrew is used to raise a weight of 2 tons. The bar of the 
jackscrew extends 2 ft. from the center of the screw. There 
are two threads to the inch. Find the force required. 

(6) Friction, Its Uses and Laws 

130. Friction, Although often inconvenient and ex- 
pensive, requiring persistent and elaborate efforts to reduce 
it to a minimum, friction has its uses, and advantages. 
Were it not for friction between our shoes and the floor or 
sidewalk, we could not keep our footing. Friction is the 
resistance that must be overcome when one body moves over 
another. It is of two kinds, sliding and rolling. If one 
draws a block and then a car of equal weight along a 
board, the force employed in each case being measured 



148 PHYSICS 

by a spring balance, a large difference in the force required 
will be noticed, showing how much less rolling friction is 
than sliding friction. 

131. Ways of Reducing Friction. (a) Friction is often 
caused by the minute projections of one surface sinking 
into the depressions of the other surface as one moves over 
the other. It follows, therefore, that if these projections 
could be made as small as possible that friction would be 
lessened. Consequently polishing is one of the best 
means for reducing friction. In machines all moving 
surfaces are made as smooth as possible. In different 
r ^ kinds of materials 
_ these little ridges 

and depressions are 

differently arranged. 
Fig. iog. The friction between R and S is fu\ j n jrjg. IOQ ^e 
greater than be ween R and T. ^ . . * * 

friction between R 
and S would be greater than between R and T. In 
R and S the surfaces will fit closer together than in R and 
T. The use of different materials will reduce friction. 
The iron axles of car wheels revolve in bearings of brass. 
Jewels are used in watches for the same reason, (c) 
Another very common method of reducing friction is by 
the use of lubricants. The oil or grease used fills up the 
irregularities of the bearing surfaces and separates them. 
Rolling friction is frequently substituted for sliding friction 
by the use of ball and roller bearings. These are used 
in many machines as in bicycles, automobiles, sewing 
machines, etc. (See Fig. no.) 

132. Value of Friction. Friction always hinders motion 
and whenever one body moves over or through another 
the energy used in overcoming the friction is transformed 
into heat which is taken up by surrounding bodies and 
usually lost. Friction is therefore the great obstacle to 



WORK AND ENERGY 



149 



perfect efficiency in machines. Friction, however, like 
most afflictions has its uses. We would find it hard to get 
along without it. Without friction we could neither walk 
nor run; no machines could be run by belts; railroad trains, 
street cars, in fact all ordinary means of travel would be 
impossible, since these depend upon friction between the 
moving power and the road for propulsion. 




Fig. 



no. Timken roller bearings. As used in the front wheel of an 
automobile. 



133. Coefficient of Friction. The ratio between the 
friction when motion is just starting and the force pushing 
the surfaces together is called the coefficient of friction. 

If the block in Fig. in is drawn along the board with 
uniform motion, the reading of the spring balances indi- 
cates the amount of friction. Suppose the friction is 
found to be 500 g., and the weight of the block to be 2000 g. 



1 50 PHYSICS 

Then the coefficient of friction for these two substances 

coo 

will be = \%, or 25 per cent. 

2000 * r 

134. Laws of Friction, Law I. The friction when motion 
is occurring between two surfaces is proportional to the force 
holding them together. Thus if one measures the friction 
when a brick is drawn along a board, he will find that it is 
doubled if a second brick is placed on the first. On 
brakes greater pressure causes greater friction. If a rope is 
drawn through the hands more pressure makes more 
friction. 




Fig. hi. A method for testing the friction between surfaces 

Law II. Friction is independent of the extent of surface 
in contact. Thus a brick has the same friction drawn on 
its side as on its edge, since, although the surface is in- 
creased, the weight is unchanged. 

Law IH. Friction is greatest at starting, but after 
starting is practically the same for all speeds. 

135. Fluid Friction. When a solid moves through a 
fluid, as when a ship moves through the water or railroad 
trains through the air, the resistance encountered is not the 
same as with solids but increases with the square of the 
velocity for slow speeds and for high speeds at a higher 
rate. This is the reason why it costs so much to in- 
crease the speed of a fast train, since the resistance of the 
air becomes the prominent factor at high speeds. The 
resistance to the motion of a ship at high speed is usually 



WORK AND ENERGY 151 

considered to increase as the cube of the velocity so that 
to double the speed of a boat its driving force must be eight 
times as great. 

Important Topics 

1. Friction: two kinds; sliding and rolling. 

2. Four ways of reducing friction. ^ 

3. Uses of friction. 

4. Coefficient of friction. Three laws of friction. 

5. Fluid friction. 

Exercises 

1. How long must an inclined plane be which is 10 meters high 
to enable a car weighing 2000 kg. to be pushed up its length 
by a force of 100 kg. parallel to the incline? 

2. State how and where friction is of use in the operation of the 
inclined plane, the wedge, the screw, the wheel and axle. 

3. A wheelbarrow has handles 6 ft. long. If a load of 300 lbs. is 
placed 18 in. from the axis of the wheel, what force placed at 
the end of the handles will be required to lift it? 

4. A jackscrew has 3 threads to the inch, and the lever used to 
turn it is 4 ft. long. If the efficiency of the screw is 60 per cent, 
what force must be applied to raise a load of 5 tons? 

5. In problem 4 how far must the force move in raising the weight 
3 in. Compute the work done upon the weight, the work done 
by the power and the efficiency of the machine from these two 
amounts of work. 

6. What simple machines are represented in a jackknife, a sewing- 
machine, a screw-driver, a plane, a saw, a table fork? 

7. A laborer carries 1500 lbs. of brick to a platform 40 ft. high. 
How much useful work does he do? 

8. If he weighs 150 lbs. and his hod weighs 10 lbs., how much use- 
less work does he do in taking 30 trips to carry up the bricks 
of problem 7? What is his efficiency? 

9. If the laborer hoists the brick of problem 7 in a bucket weighing 
50 lbs., using a fixed pulley and rope, what is the useless work 
done if it takes 12 trips to carry up the brick? What is the 
efficiency of the device? 

10. The efficiency of a set of pulleys is 70 per cent. How much 
force should be applied if acting through 100 ft. it is to raise 
a load of 400 lbs. 20 ft. ? 



152 PHYSICS 

ii. The spokes of the pilot wheel of a motor-boat are i ft. long, the 
axle around which the rudder ropes are wound is 3 in. in diameter. 
What effort must be applied if the tension in the ropes is 50 lbs.? 

12. Why are the elevated railway stations frequently placed at the 
top of an incline, the tracks sloping gently away in both 
directions? 

13. The screw of a press has 4 threads to the inch and is worked by 
a lever of such length that an effort of 25 lbs. produces a force 
of 2 tons. What is the length of the lever? 

14. It takes a horizontal force of 10 lbs. to draw a sled weighing 
50 lbs. along a horizontal surface. What is the coefficient of 
friction? 

15. The coefficient of rolling friction of a railroad train on a track 
is 0.009. What pull would an engine have to exert to haul a 
train weighing 1000 tons along a level track? 

16. How heavy a cake of ice can be dragged over a floor by a hori- 
zontal force of 20 lbs., if the coefficient of friction is 0.06? 

17. The coefficient of friction of iron on iron is 0.2. What force 
can a switch engine weighing 20 tons exert before slipping? 

18. Using a system of pulleys with a double movable block a man 
weighing 200 lbs. is just able to lift 600 lbs. What is the effi- 
ciency of the system? 

19. What is the horse-power of a pump that can pump out a cellar 
full of water 40 ft. X 20 ft. by 10 ft. deep, in 30 minutes? 

20. How many tons of coal can a 5 horse-power hoisting engine 
raise in 30 minutes from a barge to the coal pockets, a height 
of 50 ft.? 

(7) Water Power 

136. Energy of Falling Water. The energy of falling 
and running water has been used from the earliest times 
for developing power and running machinery. The 
energy is derived from the action of the moving water in 
striking and turning some form of water-wheel, several 
varieties of which are described below. 

The Overshot Wheel. The overshot wheel (Fig. 112) 
is turned by the weight of the water in the buckets. It 
was formerly much used in the hilly and mountainous 



WORK AND ENERGY 



153 



sections of this country for running sawmills and grist 
mills as it is very easily made and requires only a small 
amount of water. Its efficiency is high, being from 80 
to 90 per cent., the loss being due to friction and spilling 
of water from the buckets. To secure this high efficiency 
the overshot wheel must have 
a diameter equal to the height 
of the fall which may be as 
much as 80 or 90 ft. 

The Undershot Wheel 
The old style undershot 
wheel (Fig. 113) is used in 
level countries, where there is 
little fall, often to raise water 
for irrigation. Its efficiency is 
very low, seldom rising more 
than 25 per cent. The prin- 
ciple of the undershot wheel, 
however, is extensively used 
in the water motor and the Pel ton wheel (Fig. 114). 
In these the water is delivered from a nozzle in a jet 
against the lower buckets of the wheel. They have 




Fig. 112. Overshot water 
wheel. 




Fig. 113. Undershot 
water wheel. 




Fig. 114. Diagram illustrat- 
ing the principle of the Pel- 
ton wheel. 



an efficiency of about 80 per cent, and are much used in 
cities for running small machines, washing machines, pipe 



154 



PHYSICS 



organ blowers, etc., and in mountainous districts where 
the head is great. 

137. The Turbine. The turbine is now used more than 
any other form of water-wheel. It was invented in 1827 
by De Fourneyron in France. It can be used with a 
small or large amount of water, the power depending on 
the head (the height of the water, in the reservoir above 




Fig. 115. Diagram of a hydro-electric power house showing a vertical 
turbine A with penstock B and tail race C. 

the wheel). It is the most efficient type of water-wheel, 
efficiencies of 90 per cent, often being obtained. The 
wheel is entirely under water (Fig. 115). It is enclosed 
in an outer case (Fig. 116) which is connected with the 
reservoir by a penstock or pipe and is always kept full of 
water. The wheel itself is made in two parts, a rotating 
part called the runner (see Fig. 118) and an inner case 



WORK AND ENERGY 



155 














\o\ 




i^ e V 




fl/Hr 


\k 


~(h 




.$/ 








1 



Fig. 116. The outer case of a turbine showing the mechanism for con- 
trolling the gates. 




Fig. 117. Inner case of a turbine showing the gates and the lower end 
of the runner within. 



i56 



PHYSICS 



(Fig. 117) with gates that regulate the amount of water 
entering the . wheel. This case has blades curved so 
that the water can strike the curved blades of the rotating 




Fig. 118. The runner of a turbine. 




Fig. 119. Turbine and generator of the Tacoma hydro-electric power 

plant. 

part (Fig. 118) at the angle that is best adapted to use 
the energy of the water. The water then drops through 
the central opening into the tail race below (see Fig. 115). 



WORK AND ENERGY I 57 

The energy available is the product of the weight of the 
water and the head. The turbine is extensively used to 
furnish power for generating electricity at places where 
there is a sufficient fall of water. The electrical energy 
thus developed is transmitted from 50 to 200 miles to 
cities where it is used in running street cars, electric light- 
ing, etc. Turbines can be made to revolve about either 
vertical or horizontal axes. Fig. 119 represents a horizon- 
tal water turbine connected to a dynamo. Compare this 
with the vertical turbine in Fig. 115. 

Exercises 

1. Does a person do more work when he goes up a flight of stairs 
in 5 seconds than when he goes up in 15 seconds? Explain. 

2. A motorcycle has a 4 horse-power motor and can go at a rate 
of 50 miles per hour. Why cannot 4 horses draw it as fast? 

3. What is the efficiency of a motor that is running fast but doing 
no useful work? 

4. What horse-power can be had from a waterfall, 12 ft. high, if 
20 cu. ft. of water pass over it each second ? 

5. What is the horse-power of a fire engine if it can throw 600 
gallons of water a minute to a height of 100 ft.? 

6. Why are undershot wheels less efficient than the overshot 
wheel or turbine? 

7. A revolving electric fan is placed on the stern of a boat. Does 
the boat move? Why? Place the fan under water. Does 
the boat now move? Why? 

8. Why does an electric fan produee a breeze? 

9. Explain the action of the bellows in an organ. 

10. At Niagara Falls the turbines are 136 ft. below the surface of 
the river. Their average horse-power is 5000 each. 430 cu. 
ft. of water each second pass through each turbine. Find 
the efficiency. 

11. At Laxey on the Isle of Man is the largest overshot wheel now 
in use. It has a horse-power of 150, a diameter of 72.5 ft., a 
width of 10 ft., and an efficiency of 85 per cent. How many 
cubic feet of water pass over it each second? 



1 58 PHYSICS 

12. The power plant at the Pikes Peak Hydro-electric Company 
utilizes a head of 2150 ft., which is equal to a pressure of 935 
lbs. per square inch, to run a Pelton wheel. If the area of the 
nozzle is 1 sq. in. and the jet has a velocity of 22,300 ft. per 
minute, what is the horse-power developed if the efficiency is 
80 per cent.? 

13. A test made in 1909 of the turbines at the Centerville power 
house of the California Gas and Electric Corporation showed a 
maximum horse-power of 9700, speed 400 r.p.m. under a head 
of 550 ft. The efficiency was 86.25 per cent. How many 
cubic feet of water passed through the turbines each second? 

14. The turbine in the City of Tacoma Power Plant (see Fig. 1 20) 
uses a head of 415 ft. 145 cu. ft. a second pass through the 
turbine. Calculate the horse-power. 

15. In problem 14, what is the water pressure per square inch at 
the turbine? 

16. The power plant mentioned in problem 13 develops 6000 kw. 
What is the efficiency? 

Review Outline : Work and Energy 

Work; how measured, units, foot-pound, kilogram meter, erg. 
Energy; how measured, units, potential, P. E. = wXh,orfXs. 

Kinetic = " 

Power; how measured, units horse power, watt, 5 forms of energy, 

__ lbs. X ft. 

conservation. H.p. = 

* 550 X sec. 

Machines; 6 simple forms, 2 groups, advantages, uses, Law: W X D u 

= FXD,. 
Lever; moments, mechanical advantage, uses and applications. 
Wheel and Axle and Pulley; common applications, mechanical 

advantage. 
Inclined Plane, Wedge, and Screw; mechanical advantage and 

efficiency. 
Friction; uses, how reduced, coefficient of, laws (3). 
Water Wheels; types, efficiency, uses. 



CHAPTER VII 
HEAT, ITS PRODUCTION AND TRANSMISSION 

(i) Sources and Effects of Heat 

138. Importance of the Study of Heat. Heat is brought 
to our attention through the sensations of heat and cold. 
In winter, we warm our houses and prevent the escape of 
heat from them as much as possible. In summer we 
endeavor to keep our living rooms cool and our bodies from 
being overheated. 

A clear understanding of the several sources, effects, and 
modes of transferring heat is of importance to everyone 
living in our complex civilization, especially when we con- 
sider the multitudes of objects that have as their principal 
use the production, transfer or utilization of heat. 

139. Principal Sources of Heat. First and most im- 
portant is the Sun, which is continually sending to us 
radiant energy in the form of light and heat waves. These 
warm the earth, make plants grow, evaporate water, 
besides producing many other important effects. 

Second, chemical energy is often transformed into heat. 
One has but to think of the heat produced by burning 
coal, wood, oil, and gas, to recognize the importance of 
this source. Chemical energy is also the source of the 
heat produced within our bodies. The action of quicklime 
and water upon each other produces much heat. This 
action is sometimes employed during balloon trips as a 
means of warming things. 

Third, Electrical Energy. In many cities electric cars 
are heated by the electric current. We have all heard of 

iS9 




160 PHYSICS 

electric toasters and other devices for heating by elec- 
tricity. Electric light is pro- 
duced by the heating of some 
material to incandescence by 
an electric current. The 
electric furnace has a wide 
application in the preparation 
and refining, of metals. 

Fourth, heat is also pro- 

Fig. 1 20. Boy-scout method of duced whenever mechanical 

making fire by friction. 

energy of motion is overcome, 
whether it be by friction, concussion, or compression. 
Friction always results in the production of heat, as 
when we warm our hands by rubbing them i to- 
gether. When friction is excessive, such as in the 
case of a heavy bearing not properly oiled, the 
bearing may get very hot. This is the cause of 
the "hot box" on a railway car. Friction may 
produce heat enough to set wood on fire. Some 
fires in mills are believed to be due to this cause. 
Every boy scout must learn how to produce fire by 
friction. (See Fig. 120.) Concussion may be 
illustrated by the heating of a piece of metal by 
hammering it, while the compression of a gas 
always makes it warmer, as those who have used 
a bicycle pump have observed. The production 
of heat by compressing a gas is illustrated by 
the "fire syringe" (Fig. 121). This consists of a 
glass tube with a tightly fitted piston. A sudden 
compressiou of the air contained may ignite a 1 a x . 
trace of carbon bisulfid vapor. syringe. 

The interior of the earth is hot, but its heat 
seldom gets to the surface except at hot springs and 
volcanoes. 



HEAT, ITS PRODUCTION AND TRANSMISSION l6l 

140. The Effects of Heat. There are five important 
changes produced by heat: (a) change of size, (b) change 
of temperature, (c) change of state, as the melting of ice or 
evaporating of water, (d) chemical change, as the charring 
of sugar when it is overheated, and (e) electrical change. 
This is illustrated by the production of an electric current, 
by the heating of the junction of two different metals. A 
thermo-electric generator (see Fig. 122) has been con- 
structed upon this principle and works successfully. 




Fig. 122. A thermo-electric generator. 

Important Topics 

1. Importance of a study of heat. 

2. Four sources of heat. 

3. Five effects of heat. 

4. Examples of each. 

5. Illustrations of transformation of energy which involve thea. 

Exercises 

1. Write a list of the sources of heat in the order of their importance 
to you. State why each is important to you. 

2. Which three of the effects of heat do you make most use of? Ex- 
plain what use you make of each of these effects. 

3. Which of the forms of energy can be transformed into heat? 
How in each case? 

11 



1 62 PHYSICS 

4. Into what other forms of energy may heat be transformed? 
Name the device or process used in each case. 

5. What five different commodities are purchased by people in 
your neighborhood for the production of heat? Which of these 
costs least for the amount of heat furnished? Which is most 
expensive? How do you determine these answers? 

6. Why do many people buy heat in an expensive form, as in using 
an electric toaster, when they can obtain it in a cheaper form by 
burning gas or coal? 

7. How many of the five effects of heat have you observed outside 
of school? 

(2) Temperature and Expansion 

141. Heat and Temperature. We should now clearly 
distinguish between the terms, heat and temperature. 
Heat is a form of energy consisting of molecular motion. 
The temperature of a body is its degree of hotness. The 
amount of heat present in a body and its temperature are 
very different things. The temperature refers to the 
intensity of the heat in the body. A quart of water and a 
red hot iron ball may contain equal amounts of heat, 
although the ball has a much higher temperature than the 
water. A cup of boiling water will have the same tempera- 
ture as a tank full of boiling water, but the tank will con- 
tain more heat. Every one knows that it will take longer 
to boil a kettle full of water than a cupful. A hot-water 
bag, holding 2 quarts of water will give off heat longer than 
a 1 -quart bag, both being filled with water at the same 
temperature. To put it in another way, more work is done 
in heating a large amount of water, than a email amount 
through the same change of temperature. 

142. Units of Heat and Temperature. There are two 
common units for measuring heat: the Calorie and the 
British thermal unit. The calorie is the amount of heat 
required to raise the temperature of a gram of water one 
centigrade degree. The British thermal unit is the 



HEAT, ITS PRODUCTION AND TRANSMISSION 1 63 



amount of heat required to raise the temperature of one pound 
of water one Fahrenheit degree. One of the units plainly 
belongs to the metric system, the other to the English. 

An instrument for measuring temperature is called a 
thermometer. Various scales are placed upon thermome- 
ters. The two thermometer scales most commonly used 
in this country are the Centigrade 
and the Fahrenheit. The Fahren- 
heit thermometer scale has the 
temperature of melting ice marked 
3 2 . The boiling point or steam 
temperature of pure water under 
standard conditions of atmos- 
pheric pressure is marked 21 2 
and the space between these two 
fixed points is divided into 180 
parts. 

The centigrade thermometer 
scale has the same fixed points 
marked o and 100 and the space 
between divided into 100 parts. 
(See Fig. 123.) The centigrade 
scale is the one used by scientists scales. 
everywhere. 

143. Comparison of Thermometer Scales. It is often 
necessary to express in centigrade degrees a. temperature 
for which the Fahrenheit reading is given or vice versa. 
Since there are 180 Fahrenheit degrees between the 
"fixed points" and 100 centigrade degrees, the Fahren- 
heit degrees are smaller than the centigrade, or iF. = 
%C and iC. = q/5F. One must also take into ac- 
count the fact that the melting point of ice on the Fahren- 
heit scale is marked 32 . Hence the following rule: To 
change a Fahrenheit reading to centigrade subtract 32 



c 

1 


F 

n 




f <*>r 


1 


212 Boiling 


90 H 


1 


194" 


oH 


.... I 


176 


w| 


I 


186 


60 H 




UQ 


50 H 


~ 1 


122 


'| 




104' 


JO* 




86 


So\ 




68 


10 \ 




50 


0\ 




32 


1 


)I 


14 Freezing 


Fig. 
centigi 


123. 

ade 


Comparison of 
and Fahrenheit 



164 



PHYSICS 



and take % of the remainder, while to change centigrade 
to Fahrenheit multiply the centigrade by % and add 32 
to the product. These two rules are expressed by the 
following formulas. 



(F.-3*)5 



= C. 



oC. 



32" 



'= F. 



9 ' 5 

Another method of changing from one thermometric scale 

to another is as follows: 

A temperature of 40F. is also represented by 40C, there- 
fore to change a Fahrenheit reading into centigrade, we add 40 
to the given reading, then divide by 1.8 after which subtract 40. 
To change from a centigrade to Fahrenheit reading the only dif- 
ference in this method is to multiply by 1.8 or 

D) -40 and F.= i.8(C.+ 4 o)-40. 



C.= 



1.8 

r a 



Boiling- 



Freezing- 



212 



32 



373 



273 



144. The Absolute Scale 
of Temperature. One 

often hears the statement 
"as cold as ice." This ex- 
presses the incorrect idea 
that ice cannot become 
colder than its freezing 
temperature. The fact is 
that ice may be cooled be- 
low freezing down to the 
temperature of its sur- 
roundings. If a piece of 
ice is placed where the tem- 
perature is below the melt- 
ing point, the ice, like any 
other solid, cools to the 
temperature of the sur- 
rounding space. For example, a piece of ice out of doors 
is at ioF. when the air is at this temperature. It follows 
then, that when ice has been cooled below the freezing 



Absolute zero 



460 -273 
O 







Fig. 124. Comparison of absolute, 
centigrade and Fahrenheit scales. 



HEAT, ITS PRODUCTION AND TRANSMISSION 165 

temperature that heat is required to warm the ice up to its 
melting point; or in other words that ice at its melting 
temperature possesses some heat. The temperature at 
which absolutely no heat exists is called absolute zero. There 
has been devised an absolute scale of temperature. This 
scale is based upon the centigrade scale, i.e., with ioo 
between the two fixed points; the scale, however, extends 
down, below the centigrade zero, 273 , to what is called 
absolute zero. It follows therefore that upon the absolute 
scale, the melting point of ice, and the boiling point of 
water are 273 and 373 respectively. (See Fig. 124.) 

The means employed to find the location of absolute 
zero are of much interest. It has been observed that 
when heated a gas tends to expand. If a measured vol- 
ume of air at oC. is cooled or heated iC, it changes its 
volume ^73> the pressure remaining the same. If it is 
cooled io it loses 1 %i3> if cooled ioo it loses 10 %73 and 
so on. No matter how far it is cooled the same rate of 
reduction continues as long as it remains in the gaseous 
state. From these facts it is concluded that if the cooling 
could be carried down 273 that the volume would be re- 
duced 27 iHm or that the volume of the gas would be 
reduced to nothing. This is believed to mean that the 
molecular motion constituting heat would cease rather 
than that the matter composing the gas would disappear. 
Scientists have been able to obtain temperatures of ex- 
treme cold far down on the absolute scale. Liquid air 
has a temperature of 292 F., or i8oC. or 93 A. 
The lowest temperature thus far reported is i.7A. 
or 271. 3C, obtained in 1911, by evaporating liquid 
helium. 

145. The Law of Charles. The facts given in the last 
paragraph mean that if 273 ccm. of a gas at oC. or 273 
A. are cooled ioo, or to iooC, or i73A., then it 



1 66 PHYSICS 

will lose 10 %73 of its volume or have a volume of 173 
ccm. If warmed ioo, or up to iooC, or 373 A., it 
will have a volume of 373 ccm. It follows then that in 
every case the volume will correspond to its absolute 
temperature, providing the pressure remains unchanged. 
The expression of this fact in scientific language is called 
the law of Charles. At a constant pressure the volume of a 
given mass of gas is proportional to its absolute temperature. 

Expressed mathematically, we have ^r ~^F- " Compare 

the statement and mathematical expression of the laws of 
Charles and Boyle. 

The formulas for the laws of Boyle and Charles are 
sometimes combined into one expression as follows: 

PV P'V 

T ~ V 

or the product of the volume and pressure of a constant 
mass of gas is proportional to its absolute temperature. 

Important Topics 

1. Heat units; calorie, British thermal unit. 

2. Three thermometer scales, fixed points on each. 

3. Absolute zero, how determined. Its value on each scale. 

4. Law of Charles, its meaning. Combination of laws of Boyle 
and Charles. 

Exercises 

1. Does ice melt at the same temperature at which water freezes? 
Express the temperature of freezing water on the three ther- 
mometer scales. 

2. A comfortable room temperature is 68 F. What is this tem- 
perature on the centigrade and absolute scales? 

3. Change a temperature of i5C. to F.; isF. to C.; 4C. to F.; 
-20F. to C. 



HEAT, ITS PRODUCTION AND TRANSMISSION 167 

4. The temperature of the human body is 98.6F. What is this 
temperature on the absolute and centigrade scales? 

5. The temperature of liquid air is i8oC. What is it on the 
Fahrenheit scale? 

6. Mercury is a solid at 4oF. What is this on the centigrade 
scale? 

7. How much heat will be required to raise the temperature of 
8 lbs. of water 32F.; 5 lbs. ioF.? 



Fig. 125. A clinical thermometer used to take the temperature of the 

body. 

8. How much heat will be required to raise the temperature of 
30 g. of water 43C; 20 g^ 5oC? 

9. Compute the temperature of absolute zero on the Fahrenheit 
scale. 

10. Take three basins of water, one hot, one cold, and one lukewarm. 
If one hand be placed in the hot water while the other is placed in 
the cold and after a few minutes both are placed in the luke- 
warm water, this water will feel cool to one hand and warm to 
the other. Explain. 

11. If 200 ccm. of air at 200 absolute is heated to 3ooA. under 
constant pressure, what volume will the air occupy at the latter 
temperature? 

12. How does one change a reading on the centigrade scale to a 
corresponding reading on the absolute scale? 

(3) Expansion of Liquids and Solids 

146. Expansion of Gases. The law of Charles is found 
to apply to all gases. That is, all gases change in volume 
in proportion to the change of temperature provided the 
pressure remains constant. It is for this reason that we 
have the gas thermometer (see Fig. 126) which gives in 
skillful hands more accurate temperature readings than 
the best mercurial thermometer. Galileo devised and 
used the first air thermometer which consisted of a hollow 



1 68 PHYSICS 

bulb blown on a glass tube and inverted in a dish of water. 
(See Fig. i.) The water thermometer consists of a glass 
bulb filled with water which rises into a tube attached to 
the bulb. One disadvantage of the water thermometer 
is its limited range since it cannot be used below o or 
above ioo. Why? 

147. Expansion of Liquids. The ex- 
pansion of liquids differs from that of gases 
in several important respects : 

(a) Liquids have a smaller rate of ex- 
pansion than gases. The rate of expansion 
per degree is called the Coefficient of Ex- 
pansion. For example, the coefficient of 
expansion of a gas under constant pressure 
at oC. is 3^73 of its volume per degree 
centigrade. 

(b) Different liquids expand at wholly 

different rates, that is, their coefficients of 

expansion differ widely. For example, the 

coefficient of expansion of mercury is 0.00018 

per degree centigrade, of glycerine 0.0005 P er 

Fig. 126. Gas degree centigrade, of petroleum 0.0000 per 
thermometer. 

degree centigrade. 

(c) The same liquid often has different coefficients of 
expansion at different temperatures. Water between 
5C. and 6C. has a coefficient expansion of 0.00002 per 
degree centigrade, between 8 and 50 of 0.0006, between 
99 and ioo of 0.00076. The coefficient of expansion of 
mercury, however, is constant for a wide range of tem- 
perature and, therefore, it is well adapted for use in 
thermometers. 

148. Peculiarity in the Expansion of Water. Water 
has a peculiar rate of expansion. This is illustrated by 
the following experiment: 



HEAT, ITS PRODUCTION AND TRANSMISSION 1 69 



A test-tube filled with cold water is closed by a stopper con- 
taining a small glass tube, the water extending up into the 
small tube. (See Fig. 127.) The test-tube is placed in a freezing 
mixture of salt and ice contained in a tumbler. As the water 
cools, the level of the water in the small tube at first sinks. But 
before the water freezes it rises again, showing that 
after the water cools to a certain temperature that 
expansion of the water occurs with further cooling. 



Careful tests show that the water on cooling 
contracts until it reaches 4C. On cooling 
below this temperature it expands. For this 
reason, when the water of a lake or river 
freezes, the coldest water is at the surface. On 
account of this the ice forms at the top instead 
of at the bottom. If water contracted as it 
cooled to the freezing temperature the coldest 
water would be at the bottom. Freezing 
would begin at the bottom instead of at the 
surface. Lakes and rivers would freeze solid. 
In the summer only in shallow waters would all 
the ice melt. The result would be that fish 
and other aquatic life would be killed. Climate 
would be so changed that the earth might 
become uninhabitable. Since water is densest 
at 4C. all the water in a lake or river, when 



Fig. 127. 
Appara- 
tus used in 
testing the 



it is covered with ice, is at 4 C. except that expansion 

. , - of water, 

near the surface. 

149. The Expansion of Solids. Most solids when 
heated expand less than liquids and gases. Careful experi- 
ments show that expansion is: 

(a) Proportional to the change in temperature. 

(b) Different in different solids. 

Here are a few coefficients of linear (length) 
expansion. 



1 70 PHYSICS 

Brass 0.000018 per degree C. 

Glass 0.000009 per degree C. 

Ice 0.000052 per degree C. 

Iron 0.000012 per degree C. 

Platinum 0.000009 P er degree C. 

Zinc 0.000027 per degree C. 

The coefficient of linear expansion is the fraction of its 
length that a body expands when heated one degree. 

The coefficient of cubical expansion is the fraction of its 
volume that a body expands when heated one degree. 

The expansion of solids is used or allowed for in many 
cases : 

a. Joints between the rails on a railroad allow for the 
expansion of the rails in summer. 

b. One end of a steel truss bridge is usually supported 
on rollers so that it can expand and contract with changing 
temperatures. (See Fig. 128.) 



i [ [ yi\iMMMMi/iy 



rrr 



1, 1 1 , \ 



Fig. 1 28. Truss bridge showing roller support at one end. 

c. Suspension bridges have expansion joints where the 
ends of the iron girders can move in or out of an expansion 
joint thus making the bridge longer or shorter according 
to the temperature. 

d. Iron tires are heated, slipped on to wagon wheels 
and then cooled, the contraction on cooling setting them 
tightly in place 

e. Metallic thermometers depend upon the movement 
due to the expansion of a coiled strip of metal which turns 
a pointer on the dial of the instrument. (See Fig. 129.) 



HEAT, ITS PRODUCTION AND TRANSMISSION 171 

f. The wires that are fused into glass in incandescent 
light bulbs must have the same coefficient of expansion 
as the glass. Platinum has therefore been used for this 
purpose. (See table above.) 





Fig. 129. Metallic thermometer. 

Important Topics 

Expansion of Liquids; peculiarities. Anomalous expansion of 

water and its results. 

Expansion of solids; peculiarities, applications. 

Coefficient of linear expansion. 

Coefficient of cubical expanison. 

Exercises 

. The gas within a partly inflated balloon has a volume of 1000 
cu. ft. at a pressure of 74 cm., and a temperature of i5C. 
What will be the volume of the gas when its pressure is 37 cm. 
and the temperature is i7C? 

. A man taking a full breath on the top of a mountain fourteen 
thousand feet high inhales 4 liters of air, the pressure being 40 
cm. What volume would this same mass of air have in a 
place 600 ft. above sea-level when the barometer reads 75 cm. 
and the temperature is the same as on the mountain top? 

;. If the coefficient of linear expansion of iron is 0.000012 per 



172 PHYSICS 

degree C, how much will an iron bridge 1000 ft. long change 
in length in warming from 2oC. on a winter day to 3oC. 
upon a summer day. 

4. What are some of the results that would follow in freezing 
weather if water continually contracted on being cooled to 
zero instead of beginning to expand when cooled below 4C? 

5. Mention two instances that you have noticed of expansion 
occurring when a body is heated? 

6. Compare the density of air at 3oC. with that at ioC. at the 
same pressure. If both are present in a room, where will each 
be found? Why? 

7. Compare the density of water at 4oC. with that at ioC. If 
water at the two temperatures are in a tank, where will each be 
found? Why? 

8. If water at oC. and at 4C. are both in a tank, where will 
each be found? Why? 

9. How much heat will be required to raise the temperature of a 
cubic foot of water ioF.? 

10. How much heat will be required to raise the temperature of 
4 liters of water 2SC? 

11. How much longer would the cables of the Brooklyn suspension 
bridge be on a summer's day when the temperature is 30C. 
than in winter at 2oC, the length of cable between the sup- 
ports being about 1600 ft. 

12. If 25 liters of air at 23C. is warmed to 77C. under constant 
pressure, what will be the resulting volume of air? Explain. 

13. White pig iron melts at about 2oooF. Express this tempera- 
ture upon the centigrade and absolute scales. 

14. If 200 ccm. of air at 76 cm. pressure and 27C. temperature be 
heated to i27C. at a pressure of 38 cm. what will be the re- 
sulting volume? 

15. A balloon contains 10,000 cu. ft. of gas at 75.2 cm. pressure and 
24C. It ascends until the pressure is 18 cm. and the tem- 
perature is ioC. What is the volume of gas it then contains. 

16. A gas holder contains 50 'cu. ft." of gas at a pressure of one 
atmosphere and 62F. How much gas will it hold at 10 atmos- 
pheres and 32F. 

17. One thousand "cubic feet" of illuminating gas has what vol- 
ume with 75 lbs. pressure and temperature of ioC. 

18. Define a "cubic foot" of illuminating gas. 



HEAT, ITS PRODUCTION AND TRANSMISSION 1 73 

150. Methods of Transmitting Heat. One of the most 
practical benefits of the study of heat is clearer under- 
standing of the different methods by which heat is trans- 
ferred from one place to another and an intelligent idea 
of the means employed to prevent the transfer of 
heat. 

It should be definitely understood at the beginning that 
cold signifies the absence of heat, just as darkness implies the 
absence of light, so when one speaks of cold getting into a 
house what is really meant is either the entrance of cold 
air by some opening or else the escape of the heat. 

There are three distinct methods by which heat energy 
is transferred from one place to another, depending upon 
the medium or substance that transfers the heat. 

a. A solid transmits heat by the method called conduc- 
tion. 

b. A fluid, either a liquid or a gas, transmits heat 
mainly by the method called convection. 

c. Space transmits the energy of hot objects by the 
method called radiation. 

151. Conduction. To illustrate 
conduction, place in a gas flame the 
ends of same metal wires supported 
as in Fig. 130. In a short time the 
other ends of the wires become hot 
enough to burn one's hand. This 
may be explained as follows: The 
hot gas flame contains molecules in 
violent vibration and those striking Fig. 130. Solids con- 
the wire set its molecules rapidly duct heat, 
vibrating. Since, in a solid, the molecules are held in the 
same relative positions, when one end of a wire is heated the 
rapidly vibrating molecules at the hot end set their neigh- 
bors vibrating and these the next in turn and so on until the 




174 



PHYSICS 



whole wire is hot. It is a fortunate circumstance that 
different substances have different rates of conductivity 
for heat. To realize this, suppose that our clothing were 
as good a conductor as iron, clothing would then be very 
uncomfortable both in hot and in 
cold weather. The best conduc- 
tors for heat are metals. It is 
interesting to note that, as a rule 
good conductors of heat are also 
good conductors of electricity, 
while poor conductors of heat are 
also poor electric conductors. 
Careful experiments in testing the 
rate that heat will be. conducted 
through different substances show 
the following rates of conductivity. 
These figures are averages taken mainly from the 
Smithsonian Physical Tables: 




Fig. 131 



Water is a poor 
conductor of heat. 



Silver 100 

Copper 74 

Aluminum 35 



Brass 

Zinc 

Iron 

Tin 

German silver. 
Mercury 



7 
8.4 
i-7 



Granite 53 

Limestone 52 

Ice 5 

Glass 2 

Water 124 

Pine, with grain. .03 
Pine, across grain . 01 

Felt 008 

Air 005 



To test the conductivity of liquids, take a test-tube 
nearly full of cold water, hold the lower end in the hand 
while the tube is inclined so that the upper end is heated 
by a gas flame until the water boils. The lower end will 
be found to remain cold. (See Fig. 131.) Careful meas- 
urements of the conductivity of water show that heat is 
transmitted through it only ^00 as rapidly as in silver, 
while air conducts but 3^5 as rapidly as water. 



HEAT, ITS PRODUCTION AND TRANSMISSION 1 75 



152. Non-conductors and Their Uses. -Many solids, 
however, are poor conductors, as leather, fur, felt, and 
woolen cloth. These substances owe their non-conduc- 
tivity mainly to the fact that 
they are porous. The air 
which fills the minute spaces 
of these substances is one of 
the poorest conductors known 
and hinders the transfer of 




GLASS MBCK 



METAL NECK 




Fig. 132. Fig. 133. 

Fig. 132. Wall construction of a refrigerator. 1, Porcelain enamel 
lining lock joint; 2, inside wood lining; 3, 3-ply red rope waterproof paper; 
4, wool felt deafening paper; 5, flaxlinum insulation; 6, dead air space; 
7, flaxlinum insulation; 8, wool felt deafening paper; 9, 3-ply red rope 
waterproof paper; 10, outside wood case. 

Fig. 133. Sectional view of a Thermos bottle. 

heat through these solids. For the same reason loosely 
packed snow is a protection to vegetation covered by it 
during a period of severe cold in winter. The efficiency 



176 



PHYSICS 



of storm sash or double windows, and of the double and 
triple walls of ice-houses and refrigerators (see Fig. 132) 
in preventing the conduction of heat is also largely due 
to the poor conductivity of the air confined in the spaces 
between the walls. To prevent the circulation of the air, 
sawdust, charcoal, and other porous material is often 
loosely packed into the space between the walls of such 
structure. 

Other illustrations of effective non-conductors will occur 
to every one; such as woolen clothing, wooden handles for 
hot objects, and the packing used in fireless cookers. A 
Thermos bottle is effective as a non-conductor of heat be- 
cause the space between the double walls has the air ex- 
hausted from it (Figs. 133 and 134). 

Of several objects in a cold room, some feel much colder 
to the touch than others, thus iron, marble, oil cloth, and 
earthenware will feel colder than woolen 
cloth, carpet, feathers, or paper. The first 
four objects feel cold because they are con- 
ductors, and conduct the heat away from the 
hand rapidly. The other substances named 
are non-conductors and hence remove heat 
from the hand less rapidly, and therefore 
do not feel so cold. In a similar way, if 
several hot objects are touched by the hand, 
the good conductors are the ones which will 
burn one most quickly by conducting heat 
rapidly to the hand. The non-conductors, 
however, will rarely burn one. Why are 
the handles of hot utensils often made of non-conducting 
materials such as wood, cloth, asbestos, etc. ? 

153. Radiation is the method by which heat comes to 
us from the sun across space containing no tangible matter. 
It is also the method by which heat gets to us when we 



i \ 



Fig. 134. 
Cross-sect ion 
of the vacuum 
flask in a Ther- 
mos bottle. 



HEAT, ITS PRODUCTION AND TRANSMISSION 1 77 

stand near a fire. Everyone has noticed that this heat is 
cut off by holding an object between the person and the 
fire. This fact indicates that radiant heat travels in 
straight lines. 

The radiation of heat is believed to be accomplished by 
means of waves in a medium called ether , which is invisible 
and yet pervades everything. Three of the most impor- 
tant characteristics of radiation are first, heat is transferred 
by radiation with the speed of light, or 186,000 miles per 
second. This fact is shown by the cutting off of both 
the sun's heat and light at the same instant during an 
eclipse of the sun. Second, radiant heat 1 travels in straight 
lines, while other modes of transferring heat may follow 
irregular paths. The straight line motion of radiant heat 
is shown by its being cut off where a screen is placed be- 
tween the source of heat and the object sheltered. Third, 
radiant heat may pass through an object without heating it. 
This is shown by the coldness of the upper layers of the 
atmosphere and also by the fact that a pane of glass may 
not be heated appreciably by the heat and light from the 
sun which passes through it. 

When radiant energy falls upon any object it may be 
(a) reflected at the surface of the object, (b) transmitted 
through the substance, (c), absorbed. All three of these 
effects occur in different degrees with different portions 
of the radiation. Well-polished surfaces are good reflectors. 
Rough and blackened surfaces are good absorbers. Trans- 
parent objects are those which transmit light well, but 
even they absorb some of the energy. 

154. The Radiometer. Radiant heat may be detected, 
by means of the radiometer (Fig. 135). This consists of 
a glass bulb from which the air has been nearly exhausted. 

'Radiant heat is really radiant energy and becomes heat when it is 
absorbed by a body. 
12 



i 7 8 



PHYSICS 




Within it is a wheel with four vanes of mica or of alumi- 
num mounted on a vertical axis. One side of each vane is 
covered with lampblack, the other being highly polished. 
When exposed to radiant heat from any source the vanes 
revolve with the bright side in advance. 

The bulb is so nearly exhausted of air 
that a single molecule remaining may travel 
from the walls of the bulb to the vanes 
without coming in contact with another 
molecule. 

The blackened sides absorb more heat 
than the highly polished sides. The air 
molecules striking these blackened sides re- 
ceive more heat and so rebound with 
greater velocity than from the other side, 
thus exerting greater pressure. The black- 
ened sides therefore are driven backward. 
If the air were not so rarined the air 
molecules would hit each other so fre- 
quently as to equalize the pressure and there would be no 
motion. 

Sun's Radiation. Accurate tests of the amount of the 
sun's radiation received upon a square centimeter of the 
earth's surface perpendicular to the sun's rays were made 
at Mt. Wilson in 19 13. The average of 690 observations 
gave a value of 1.933 calories per minute. These results 
indicate that the sun's radiation per square centimeter is 
sufficient to warm 1 g. of water i.933C. each minute. 
Although the nature of radiation is not discussed until 
Art. 408-411 in light, it should be said here that all bodies 
are radiating heat waves at all temperatures, the heat 
waves from cool bodies being much longer than those from 
hot bodies. Glass allows the short luminous waves to 
pass through freely but the longer heat waves from objects 



Fig. i3'5. A 
radiometer. 



HEAT, ITS PRODUCTION AND TRANSMISSION 1 79 

at the room temperature pass through with difficulty. 
This is the reason why glass is used in the covering of 
greenhouses and hot beds. Water also absorbs many of 
the longer heat waves. It is therefore used in stereopti- 
cons to prevent delicate lantern slides from being injured 
by overheating. 

Important Topics 

1. Conduction in solids, liquids, gases. 

2. Non-conductors; uses, best non-conductors. 

3. Radiation, three characteristics. 

4. The sun's radiation, amount. The radiometer. 

Exercises 

1. Does clothing ever afford us heat in winter? How then does 
it keep us warm? 

2. Why are plants often covered with paper on a night when 
frost is expected? 

3. Will frost form in the fall of the year sooner on a wooden or 
a cement sidewalk? Why? On which does ice remain longer? 
Why? 

4. Why in freezing ice-cream do we put the ice in a wooden pail 
and the cream in a tin one? 

5. Is iron better than brick or porcelain as a material for stoves? 
Explain. 

6. Which is better, a good or a poor conductor for keeping a 
body warm? for keeping a body cool? 

7. Should the bottom of a teakettle be polished? Explain. 

8. How are safes made fireproof? 

9. Explain the principle of the Thermos bottle. 

10. Explain why the coiled wire handles of some objects as stove- 
lid lifters, oven doors, etc., do not get hot. 

(5) Transmission of Heat in Fludds. Heating 
and Ventilation 

155. Convection. While fluids are poor conductors, 
they may transmit heat more effectively than solids by 
the mode called convection. To illustrate: if heat is 



i8o 



PHYSICS 






-5: 



3\Y/t 













applied at the /o/> of a test-tube of water, the hot water 
being lighter is found at the top, while at the bottom the 
water remains cold. On the other hand, if heat is applied 
at the bottom of the vessel, as soon as the water at the bot- 
tom is warmed (above 4C.) it expands, becomes lighter 
and is pushed up to the top by the colder, denser water 

about it. This circulation of 
water continues as long as heat 
is applied below, until all of the 
water is brought to the boiling 
temperature. (See Fig. 136.) 

When a liquid or a gas is 
heated in the manner just 
described, the heat. is said to 
be .transferred by convection. 
Thus the air in the lower part 
of a room may receive heat by 
conduction from a stove or 
radiator. As it expands on 
being warmed, it is pushed up 
by the colder denser air about 
it, which takes its place, thus 
creating a circulation of the air 
in the room. (See Fig. 137.) 
The heated currents of air give 
up [their heat to the objects in the room as the circulation 
continues. These air currents may be observed readily 
by using the smoke from burning "touch paper" (unglazed 
paper that has been dipped into a solution of potassium 
nitrate ["saltpeter"] and dried). 

156. Draft of a Chimney. When a fire is started in a 
stove or a furnace the air above the fire becomes heated, 
expands, and therefore is less dense than it was before. 
This warm air and the heated gases which are the products 



Fig. 



136. Convection 
liquid. 



HEAT, ITS PRODUCTION AND TRANSMISSION 



Itfl 



of the combustion of the fuel weigh less than an equal 
volume of the colder air outside. Therefore they are 
pushed upward by a force equal to the difference between 
their weight and the weight of an equal volume of the 
colder air. 

The chimney soon becomes filled with these heated 
gases. (See Fig. 138.) These are pushed upward by the 



n 

^ t 
t 

(t 



r =i> 


V 

UA 1 




Fig. 137. Convection currents in a room. Fig. 138. Fire place 

showing draft of a 
chimney. 

pressure of the colder, denser air, because this colder air 
is pulled downward more strongly by the force of gravity 
than are the heated gases in the chimney. 

Other things being equal, the taller the chimney, the 
greater the draft, because there is a greater difference 
between the weight of the gases inside and the weight of 
an equal volume of outside air. 

157. Convection Currents in Nature. Winds are pro- 
duced by differences in the pressure or density of the air, 
the movement being from places of high toward places of 
low pressure. One of the causes of a difference in density 



1 82 PHYSICS 

of the air is a difference in temperature. This is illus- 
trated by what are called the land and sea breezes along the 
sea shore or large lakes. During the day, the temperature 
of the land becomes higher than that of the sea. The air 
over the land expands and being lighter is moved back and 
upward by the colder, denser air from the sea or lake. 
This constitutes the sea breezes (Fig. 139). At night the 
land becomes cooler much sooner than the sea and the 
current is reversed causing the land breeze. (See Fig. 140.) 





Fig. 139. Sea breeze. Fig. 140. Land breeze. 

The trade winds are convection currents moving toward 
the hot equatorial belt from both the north and the south. 
In the hot belt the air rises and the upper air flows back 
to the north and the south. This region of ascending 
currents of air is a region of heavy rainfall, since the satu- 
rated air rises to cool altitudes where its moisture is con- 
densed. The ocean currents are also convection currents. 
Their motion is due to prevailing winds, differences in 
density due to evaporation and freezing, and to the rota- 
tion of the earth, as. well as to changes in temperature. 

158. The heating and ventilation of buildings and the 
problems connected therewith are matters of serious con- 
cern to all who live in winter in the temperate zone. Not 
only should the air in living rooms be comfortably heated, 
but it should be continually changed especially in the 
crowded rooms of public buildings, as those of schools, 
churches, and assembly halls, so that each person may be 
supplied with 30 or more cubic feet of fresh air per minute. 
In the colonial days, the open fire place afforded the ordi- 



HEAT, ITS PRODUCTION AND TRANSMISSION 



l8 3 



nary means for heating rooms. This heated the room 
mainly by radiation. It was wasteful as most of the heat 
passed up the chimney. This mode of heating secured 
ample ventilation. Fire places are sometimes built in 
modern homes as an aid to ventilation. 

Benjamin Franklin seeing the waste of heat in the open 
fire places devised an iron box to contain the fire. This 
was placed in the room and provided heat by conduction, 
convection, and radiation. It was called Franklin's 
stove and in many forms is still commonly used. It saves 
a large part of the heat produced by burning the fuel and 
some ventilation is provided by its draft. 

159. Heating by Hot Air. The presence of stoves in 
living rooms of homes is accompanied by the annoyance of 




Fig. 141. Heating and ventilating by means of a hot-air furnace. 

scattered fuel, dust, ashes, smoke, etc. One attempt to 
remove this inconvenience led to placing a large stove or 
fire box in the basement or cellar, surrounding this with a 
jacket to provide a space for heating air which is then 
conducted by pipes to the rooms above. This device is 
called the hot-air furnace. (See Fig. 141.) The heated 



184 



PHYSICS 



air rises because it is pushed up by colder, denser air which 
enters through the cold-air pipes. The hot-air furnace 
provides a good circulation of warm air and also ventila- 
tion, provided some cold air is admittd to the furnace from 
the outside. One objection to its use is that it may not 




Fig. 142. A hot-water system of heating. 

heat a building evenly, one part being very hot while 
another may be cool. To provide even and sufficient 
heat throughout a large building, use is made of hot water 
or steam heating. 



HEAT, ITS PRODUCTION AND TRANSMISSION 1 85 




i86 



PHYSICS 



1 60. Hot- water Heating. In hot-water heating a fur- 
nace arranged for heating water is placed in the basement. 
(See Fig. 142.) Attached to the top of the heater are pipes 
leading to the radiators in the various rooms; other pipes 
connect the radiators to the bottom of the boiler. The 
heater, pipes, and radiators are all filled with water before 
the fire is started. When the water is warmed, it expands 
and is pushed up through the pipes by the colder water in 
the return pipe. The circulation continuing brings hot 
water to the radiator while the cooled water returns to the 
heater, the hot radiators heating the several rooms. 

161. Steam Heating. In steam heating a steam boiler 
is connected to radiators by pipes. (See Fig. 143.) The 
steam drives the air out of the pipes and radiators and 
serves as an efficient source of heat. Heating by steam is 
quicker than heating with hot water. It is therefore pre- 
ferred where quick, efficient heating is required. Hot 

water is less intense 
and more economical 
in mild weather and 
is often used in pri- 
vate homes. 

162. Direct and 
Indirect Heating. 
In heating by direct 
radiation (Figs. 142, 
Fig. 144. Heating by an indirect radiator 143), the steam or 
with side-wall register. hot-water radiators 

are placed in the rooms to be heated. With direct 
radiation, ventilation must be provided by special means, 
such as opening windows, doors, and ventilators. Some- 
times radiators are placed in a box or room in the base- 
ment. Air from out of doors is then driven by a fan 
over and about the hot radiators. The air thus heated 




HEAT, ITS PRODUCTION AND TRANSMISSION 1 87 




-An automatic 

valve. 



is conducted by pipes to the several rooms. This ar- 
rangement is called indirect 
heating. (See Fig. 144.) The 
latter method, it may be ob- 
served, provides both heat and 
ventilation, and hence is often 
used in schools, churches, court 
houses, and stores. Since heated 
air, especially in cold weather, 
has a low relative humidity some 
means of moistening the air of 
living rooms should be pro- 
vided. Air when too dry is 
injurious to the health and FlG - J 45- 
also to furniture and wood 
work. The excessive drying of wood and glue in a piece 
of furniture often causes it to fall apart. 

163. Vacuum Steam Heating. In steam heating, air 

valves (Fig. 145) are 
placed on the radi- 
ators to allow the 
air they contain to 
escape when the 
steam is turned on. 
When all the air is 
driven out the valve 
closes. Automatic 
vacuum valves (Fig. 
146) are sometimes 
used. When the fire 
is low and there is no 
steam pressure in the 
Fig. 146. An automatic vacuum valve. radiators the pressure 

of the air closes the valve, making a partial vacuum 




1 88 



PHYSICS 



inside. The boiling point of water falls as the pressure 
upon it is reduced. As water will not boil under ordi- 
nary atmospheric pressure until its temperature is iocC. 
(2i2F.), it follows that by the use of vacuum systems, 
often called vapor systems, of steam heating, water will be 
giving off hot vapor even after the fire has been banked for 
hours. This results in a considerable saving of fuel. 
164. The Plenum System of Heating. In the plenum 




FjG. 147. Plenum hot-blast system with temperature regulation. 



system of heating (see Fig. 147) fresh air is drawn through 
a window from outdoors and goes first through tempering 
coils where the temperature is raised to about 70 . The 
fan then forces some of the air through heating coils, 
where it is reheated and raised to a much higher tempera- 
ture, depending upon the weather conditions. Both 
the hot and tempered air are kept under pressure by the 
fan in the plenum room and are forced from this room 
through galvanized iron ducts to the various rooms to be 



HEAT, ITS PRODUCTION AND TRANSMISSION 1 89 

heated. The foul air is forced out of the room through 
vent ducts which lead to the attic where it escapes through 
ventilators in the roof. 

A thermostat is placed in the tempered-air part of the 
plenum room to maintain the proper temperature of the 
tempered air. This thermostat operates the by-pass 
damper under the tempering coils, and sometimes the 





a b 

Fig. 148. A thermostat. (Johnson System.) 

valves on the coils. The mixing dampers at the base 
of the galvanized-iron ducts are controlled by their re- 
spective room thermostats. Attic-vent, fresh-air, and 
return-air dampers are under pneumatic switch control. 
A humidifier can be provided readily for this system. 
This system of heating is designed particularly for school 
houses where adequate ventilation is a necessity. 

165. The Thermostat. One of the many examples of 
the expansion of metals is shown in one form of the thermo- 
stat (Fig. 148) in which two pieces of different metals 



190 PHYSICS 

and of unequal rates of expansion, as brass and iron, are 
securely fastened together. 

The thermostatic strip T moving inward and outward, 
as affected by the room temperature, varies the amount of 
air which can escape through the small port C. When the 
port C is completely closed (Fig. 148a) the full air pfessure 
collects on the diaphragm B which forces down the main 
valve, letting the compressed air from the main pass 
through the chamber D into chamber E as the valve is 
forced off its seat. The air from chamber E then passes 
into the branch to operate the damper. 

When port C is fully open (Fig. i486) the air pressure 
on diaphragm B is relieved, the back pressure in E lifts 
up the diaphragm and the air from the branch escapes out 
through the hollow stem of the main valve, operating the 
damper in the opposite direction from that when C is 
closed. 

Important Topics 

1. Transmission of heat in fluids. 

2. Convection. Drafts of a chimney. Land and sea breezes. 

3. Heating and ventilation of buildings. 

(a) By hot air. 

(b) Hot-water heating. 

(c) Steam heating. 

(d) Direct and indirect heating. 

(e) Vacuum steam heating. 

(f) The plenum system. 

(g) The thermostat. 

Exercises 

1. Is a room heated mainly by conduction, convection, or radiation, 
from (a) a stove, (b) a hot-air furnace, (c) a steam radiator? 

2. Name three natural convection currents. 

3. Explain the draft of a chimney. What is it? Why does it 
occur? 



HEAT, ITS PRODUCTION AND TRANSMISSION 191 

4. Make a cross-section sketch of your living room and indicate 
the covection currents by which the room is heated. Explain 
the heating of the room. 

5. Make a sketch showing how the water in the hot-water tank 
in the kitchen or laundry is heated. Explain your sketch, 
indicating convection currents. 

6. Is it economical to keep stoves and radiators highly polished? 
Explain. 

7. If you open the door between a warm and a cool room what will 
be the direction of the air currents at the top and at the bottom 
of the door? Explain. 

8. If a hot-water heating system contains 100 cu. ft. of water 
how much heat will be required to raise its temperature isoF.? 

9. Why does a tall chimney give a better draft than a short one? 

10. Explain how your school room is heated and ventilated. 

11. Should a steam or hot- water radiator be placed near the floor 
or near the ceiling of a room? Why? 

12. In a hot-water heating system an open tank connected with the 
pipes is placed in the attic or above the highest radiator. 
Explain its use < 

(6) The Moisture in the Atmosphere, 
Hygrometry 

166. Water Vapor in the Air. The amount of water 
vapor present in the air has a marked effect upon the 
weather and the climate of a locality. The study of the 
moisture conditions of the atmosphere, or hygrometry, 
is therefore a matter of general interest and importance. 
The water vapor in the atmosphere is entirely due to 
evaporation from bodies of water, or snow, or ice. In the 
discussion of evaporation, it is described as due to the 
gradual escape of molecules into the air from the surface 
of a liquid. This description fits exactly the conditions 
found by all careful observers. Since the air molecules 
are continually striking the surface of the liquid, many of 
them penetrate it and become absorbed. In the same 
manner many vapor molecules reenter the liquid, and if 



192 PHYSICS 

enough vapor molecules are present in the air so that as 
many vapor molecules reenter the liquid each second as 
leave it, the space above the liquid is said to be saturated 
as previously described. (See Art. 18.) 

167. Conditions for Saturation. If a liquid is evapo- 
rating into a vacuum, the molecules on leaving find no 
opposition until they reach the limits of the vessel contain- 
ing the vacuum. Evaporation .under these conditions 
goes on with great rapidity and the space becomes satu- 
rated almost instantly. If, however, air be present at 
ordinary pressure, many of the ordinary water vapor 
molecules on leaving are struck and returned to the water 
by the air molecules directly above. Those escaping 
gradually work their way upward through the air. This 
explains why it is that our atmosphere is not often satu- 
rated even near large bodies of water, the retarding 
effect of the air upon the evaporation preventing more 
than the layers of air near the water surface becoming 
saturated. 

Just as the amount of salt that can be held in solution 
in a liquid is lessened by cooling the solution (Art. 26), so 
the amount of water vapor that can be held in the air is 
lessened by lowering its temperature. If air not moist 
enough to be saturated with water vapor is cooled, it will, 
as the cooling continues, finally reach a temperature at 
which it will be saturated or will contain all the water 
vapor it can hold at this temperature. If the air be still 
further cooled some of the water vapor will condense and 
may form fog, dew, rain, snow, etc., the form it takes 
depending upon where and how the cooling takes place. 
. 168. The Formation of Dew. If the cooling of the 
atmosphere is at the surface of some cold object which 
lowers the temperature of the air below its saturation 
point, some of its moisture condenses and collects upon the 



HEAT, ITS PRODUCTION AND TRANSMISSION 193 

cold surface as dew. This may be noticed upon the surface 
of a pitcher of ice-water in summer. At night, the tem- 
perature of grass and other objects near or on the ground 
may fall much faster than that of the atmosphere owing to 
the radiation of heat from these objects. If the tempera- 
ture falls below the saturation point, dew will be formed. 
This natural radiation is hindered when it is cloudy, there- 
fore little dew forms on cloudy nights. Clear nights help 
radiation, therefore we have the most dew on nights when 
the sky is clear. If the temperature is below freezing, 
frost forms instead of dew. 

169. Formation of Fog. If the cooling at night is great 
enough to cool the body of air near the earth below the 
saturation temperature, then not only may dew be formed, 
but some moisture is condensed in the air itself, usually 
upon fine dust particles suspended in it. This constitutes 
a fog. If the cooling of the body of air takes place above 
the earth's surface as when a warm moist current of air 
enters a colder region, e.g., moves over the top of a cold 
mountain, or into the upper air, then as this air is cooled 
below its saturation point, condensation upon fine sus- 
pended dust particles takes place, and a cloud is formed. 
If much moisture is present in the cloud, the drops of 
water grow in size until they begin to fall and rain results; 
or if it is cold enough, instead of rain, snowflakes will be 
formed and fall. Sometimes whirling winds in severe 
thunderstorms carry the raindrops into colder and then 
warmer regions, alternately freezing and moistening the 
drops or bits of ice. It is in this way that hail is said to be 
formed. 

170. The Dew Point. The temperature to which air 

must be cooled to saturate it or the temperature at which 

condensation begins is called the dew point. This is often 

determined in the laboratory by partly filling a polished 
13 
t 



194 



PHYSICS 



metal vessel with water and cooling the water by adding 
ice until a thin film of moisture is formed upon the outer 
surface. The temperature of the surface when the mois- 
ture first forms is the dew point. 

171. The Humidity of the Atmosphere. After the dew 
point has been obtained, one may compute the relative 
humidity or degree of saturation of the atmosphere, from the 
table given below. This is denned as the ratio of the 
amount of water vapor present in the air to the amount that 
would be present if the air were saturated at the same 
temperature. 

For example, if the dew point is 5C. and the temperature of 
the air is 22C, we find the densities of the water vapor at the two 
temperatures, and find their ratio: 6.8/19.3 = 35 per cent, nearly. 
Determinations of humidity may give indication of rain or frost and 
are regularly made at weather bureau stations. They are also 
made in buildings such as greenhouses, hospitals, and schoolhouses 
to see if the air is moist enough. For the most healthful conditions 
the relative humidity should be from 40 per cent, to 50 per cent. 

Weight of Water (w) in Grams Contained in i Cubic Meter of 
Saturated Air at Various Temperatures (*)C. 



1 / c 


w 


fC. 


w 


tC. 


w 


/C. 


w 


10 


2. 1 





4.9 


10 


9-4 


20 


17.2 


- 9 


2 


4 


1 


5 


2 


11 


10. 


21 


18.2 


- 8 


2 


7 


2 


5 


6 


12 


10.6 


22 


19-3 


- 7 


3 





3 


6 





13 


n-3 


23 


20.4 


- 6 


3 


2 


4 


6 


4 


14 


12.0 


24 


21.5 


- 5 


3 


5 


5 


6 


8 


15 


12.8 


25 


22.9 


- 4 


3 


8 


6 


7 


3 


16 


13.6 


26 


24.2 


- 3 


4 


1 


7 


7 


7 


17 


14-5 


27 


25.6 


2 


4 


4 


8 


8 


1 


18 


i5-i 


28 


27.0 


1 


4 


6 


9 


8 


8 


19 


16.2 


29 


28.6 





4 


9 


10 


9 


4 


20 


17.2 


30 


30.1 



172. Wet and Dry Bulb Hygrometer. A device for 
indicating the relative humidity of the air is called an 



HEAT, ITS PRODUCTION AND TRANSMISSION 195 



hygrometer. There are various forms. The wet and dry 
bulb hygrometer is shown in Fig. 149. This device con- 
sists of two thermometers, one with its bulb dry and ex- 
posed to the air, the other bulb being kept continually 
moist by a wick dipping into a vessel of water. An 
application of the principle of cooling by evaporation is 
made in this instrument. Unless the air is saturated so 

that evaporation is prevented, 
the wet-bulb thermometer 
shows a lower temperature, the 
difference depending upon the 
amount of moisture in the air, 
or upon the relative humidity. 
Most determinations of relative 





Fig. 149. Wet and dry bulb Fig. 150. A dial hygrometer, 

hygrometer. 

humidity are made with this kind of instrument. It is 
necessary in order to make an accurate determination, 
to fan or set the air in motion about the thermometers 
for some time before reading them. The relative humidity 
is then found by using tables giving the relative humidity 
that corresponds to any reading of the thermometers. 

A form of hygrometer in common use is shown in Fig. 150. In 
this device, a thin strip of hygroscopic material (as a piece of goose 
quill) is formed into a spiral coil. One end of this is fastened to a 
post. The other end carried a hand or pointer. The latter moves 



196 PHYSICS 

over a printed scale and indicates directly the relative humidity. 
Its indications should be tested by comparing its readings with the 
results of dew-point determinations. The position of the pointer 
may be adjusted by turning the post. 

Important Topics 

1. Water vapor in the air. Cause and effect. 

2. Formation of dew, fog, rain, and snow. 

3. Dew point, relative humidity. 

4. Use of the dry- and wet-bulb hygrometer. Goose-quill 
hygrometer. 

Exercises 

1. How is the relative humidity of the air affected by warming it? 
Explain. 

2. How does the white cloud of steam seen about a locomotive in 
cold weather differ from fog? Explain. 

3. In cold weather is the relative humidity of air out of doors 
and indoors the same? Explain. 

4. Compare the relative humidity of air in a desert and near the 
ocean. 

5. Look up the derivation of the term "hygrometer." Give the 
use of the instrument. 

6. Find the relative humidity of air at 2oC. if its dew point is 
at ioC. 

7. How may the relative humidity of the air in a home be increased ? 

8. What is the effect of high humidity in the summer upon human 
beings? How do you explain this? 

9. Does dew fall? Explain how dew is formed? 

10. In what respects is a cloud similar to a fog? In what respects 
different? 

11. Why are icebergs frequently enveloped in fog? 

12. Does dew form in the day time? Explain. 

(7) Evaporation 
173. Effects of Evaporation. In Art. 19 the cooling 
effect of evaporation is mentioned and some explanation 
is made of the cooling effect observed. Since evaporation 
is employed in so many ways, and since its action is simply 
explained by the study we have made of molecular motions 



HEAT, ITS PRODUCTION AND TRANSMISSION 197 

and molecular forces, it may be well to consider this 
subject further. 

Take three shallow dishes, and place in one a little water, in 
another some alcohol, and some ether in the third, the liquids being 
taken from bottles that have stood several hours in the room so 
that all are at the same temperature. After a short time take the 
temperature of the three liquids. Each will be at a lower tem- 
perature than at first, but of the three the ether will be found to be 
the coolest, alcohol next, and the water nearest its first temperature. 
It will be noticed also that the ether has evaporated most in the 
same time. Similar effects may be observed by placing a few drops 
of each of these three liquids upon the back of one's hand, or by 
placing a few drops in turn upon the bulb of a simple air thermometei 

174. Cooling Effect of Evaporation. The molecules 
that leave an evaporating liquid are naturally the swiftest 
moving ones, that is, the ones having the highest tempera- 
ture, so their escape leaves the liquids cooler than before, 
and the one whose molecules leave fastest is naturally the 
one that becomes coldest, that is, the ether, in the experi- 
ment of Art. 173. If no air pressure were exerted upon 
the surface of the liquid, the escape of the molecules would 
be much increased and the temperature of the liquid 
would be lowered rapidly. 

To test this, fill a thin watch glass with ether and place it over a 
thin slip of glass with a drop of cold water between the two. Now 
place this apparatus under the receiver of an air pump and exhaust 
the air. The rapid evaporation of the ether so lowers its tempera- 
ture, that often the drop of water is frozen. The lowest tempera- 
tures are obtained by evaporating liquids at reduced pressure. 

Onnes by evaporating liquid helium at a pressure of 
about 1.2 mm. reached the lowest temperature yet at- 
tained, 456F., or 27i.3C. 

If four thermometers are taken, the bulbs of three being wetted 
respectively with ether, alcohol, and water the fourth being dry, on 
vigorously fanning these, the moistened thermometers show that 
they have been cooled while the dry one is unaffected. 



198 PHYSICS 

This indicates that fanning a dry body at the tempera- 
ture of the air does not change its temperature. Fanning 
does increase evaporation by removing the air containing 
the evaporated molecules near the surface of the liquid 
so that unsaturated air is continually over the liquid. If 
a pint of water is placed in a bottle and another pint in a 
wide pan the latter will become dry much sooner because 
of the greater surface over which evaporation can take 
place. Application of this is made at salt works where 
the brine is spread out in shallow pans. 

175. Rate of Evaporation. The rate of evaporation is 
affected by several factors. These have been illustrated 
in the preceding paragraphs. To briefly summarize: 

The rate of evaporation of a liquid is affected by 

(a) The nature of the liquid. 

(b) The temperature of the liquid. 

(c) The pressure upon its evaporating surface. 

(d) The degree of saturation of the space into which 
the liquid is evaporating. 

(e) The rate of circulation of air over its surface. 

(f) The extent of surface exposed to evaporation. 

176. Molecular Motion in Solids. Evidence of molecu- 
lar motion in liquids is given by expansion on heating, 
evaporation, and diffusion. Do any of these lines of 
evidence apply to solids? It is a fact of common experi- 
ence that solids do become larger on heating. Spaces 
are left between the ends of rails on railroads so that 
when they expand in summer they will not distort the 
track. Iron tires are placed on wheels by heating them 
until they slip on easily. Then on cooling, the iron shrinks 
and presses the wheel tightly. Many common demon- 
strations of expansion are found in lecture rooms. The 
fact of the evaporation of a solid is often detected by notic- 
ing the odor of a substance. The odor of moth balls is 



HEAT, ITS PRODUCTION AND TRANSMISSION 1 99 

one example. Camphor also evaporates. Heated tin has 
a characteristic odor noted by many. Ice and snow 
disappear in winter even though the temperature is below 
freezing. Wet clothes "freeze dry/' that is, dry after 
freezing, by evaporation. A few crystals of iodine placed 
in a test-tube and gently heated form a vapor easily seen, 
even though none of the iodine melts. Where the vapor 
strikes the side of the tube, it condenses back to dark gray 
crystals of iodine. This change from solid directly to gas 
and back again without becoming liquid is called sublima- 
tion. A number of solids are purified by this process. 

Important Topics 

1. Cooling effect of evaporation, rate of evaporation affected by 
six conditions. 

2. Effects of molecular motion in solids: (a) Expansion, (b) Evap- 
oration, (c) Sublimation. 

Exercises 

1. Does sprinkling the streets or sidewalks cool the air? Why? 

2. Give an illustration for each of the factors affecting evaporation. 

3. Give an illustration for each of the three evidences of molecu- 
lar motions in solids. 

4. Since three-quarters of the earth's surface is covered with water, 
why is not the air constantly saturated? 

5. If the air has the temperature of the body, will fanning the 
perfectly dry face cool one? Explain. Will the effect be the 
same if the face is moist? Explain. 

6. What is the cause of "Cloud Capped" mountains? 

7. Why does the exhaust steam from an engine appear to have so 
much greater volume on a cold day in winter than on a warm one 
in summer? 

8. What causes an unfrozen pond or lake to "steam" on a very 
cold day in winter, or on a very cool morning in summer? 

9. As the air on a mountain top settles down the sides to places of 
of greater pressure, how will its temperature be affected? its 
relative humidity? Explain. 

10. On our Pacific coast, moist winds blow from the west over the 
mountains. Where will it rain? Where be dry? Explain. 



CHAPTER VIII 
HEAT AND WORK 



(i) Heat Measurement and Specific Heat 

177. Specific Heat. In the study of density and specific 
gravity it is made clear that different substances differ 
widely in the amount of matter contained in equal vol- 
umes, e.g., lead is much denser than water. The study of 
the relative densities of substance is usually considered 
under the subject of specific gravity. 

Specific heat as distinguished from specific gravity is 
concerned with the capacity for heat possessedby different 
substances. The definition for specific heat is: The 
ratio of the amount of heat required to change the tempera- 
ture of a given mass of a substance 1 C. degree to the amount 
of heat required to change the temperature of the same mass 
of water 1 C. degree. By definition, it requires 1 calorie to 
raise the temperature of the gram of water iC. The 
specific heat therefore of water is taken as one. The 
specific heat of most substances except hydrogen, is less 
than that of water, and as a rule, the denser the body the 
less its specific heat, as may be observed in the following 
table : 



Specific 


Specific 


gravity 


heat 


19-3 


0.032 


13.6 


0.033 


8.9 


0.093 


8.4-8.9 


0.094 


8. 57 


0. 11 


7-5+ 


0.1125 



Specific 
gravity 



Specific 
heat 



Gold. . . . 
Mercury 
Copper . 

Brass 

Nickel. . 
Iron .... 



Aluminum 

Glass 

Ice 

Air 

Steam 
Hydrogen. 



2.67 

2.5-3-6 

0.918 

0.00129 

o.oco6i 

0.00009 



0.218 
o. 19 
0.504 
0.23'/ 
0.480 
3 409 



HEAT AND WORK 201 

178. Method of Determining Specific Heat. The 

specific heat of a body is usually determined by what is 
called the method of mixtures. 

For example, a definite weight of a substance, say a 200-g. iron 
ball, is placed in boiling water until it has the temperature of the 
hot water, iooC. Suppose that 300 g. of water at i8C. be placed 
in a calorimeter, and that the hot iron ball on being placed in the 
water raises its temperature to 23.5C. The heat received by the 
water equals 5.5 X 300 = 1650 calories. This must have come 
from the heated iron ball. 200 g. of iron then in cooling 76.5C. 
(ioo 23. 5 ) gave out 1650 calories. Then 1 g. of iron in cooling 
76.5C. would give out 8.25 calories or 1 g. of iron cooling iC. 
would yield about o.n calorie. The specific heat of the iron is 
then o.n. For accurate determination the heat received by the 
calorimeter must be considered.- 

179. Heat Capacity of Water. The large capacity for 
heat shown by water is useful in regulating the temperature 
of the air near lakes and the ocean. In hot weather the 
water rises slowly in temperature absorbing heat from the 
warm winds blowing over it. In winter the large amount 
of heat stored in the water is slowly given out to the air 
above. Thus the climate near the ocean is made more 
moderate both in winter and summer by the large capacity 
of water for heat. This large heat capacity of water may 
seem to be a disadvantage when one is warming it for 
domestic purposes since it requires so much heat to warm 
water to boiling. However, it is this capacity that makes 
hot-water bottles and hot-water heating effective. 

If one takes a pound of ice at oC. in one dish and a pound of 
water at oC. in another, and warms the dish of ice by a Bunsen 
flame until the ice is just melted, and then warms the water in the 
other dish for the same time, the water will be found to be hot and 
at a temperature 8oC, or i76F. 

180. The Heat of Fusion of Ice. This experiment indi- 
cates the large amount of heat required to change the ice 
to water without changing its temperature. As indicated 



202 PHYSICS 

by the experiment, it requires 80 calories to melt 1 g. of 
ice without changing its temperature or, in other words, 
if one placed 1 g. of ice at oC. in 1 g. of water at 8oC, 
the ice would be melted and the water would be cooled to 
oC. 4, 

181. Heat Given out by. Freezing Water. Just as 80 
calories of heat are required to melt 1 g. of ice, so in freez- 
ing 1 g. of water, 80 calories of heat are given out. 

The fact that heat is set free or given out when a liquid solidifies 
may be strikingly shown by making a strong solution of sodium 
acetate. On allowing this to cool quietly it will come to the room 
temperature and remain liquid. If now a small crystal of sodium 
acetate is dropped into the liquid the latter quickly becomes a solid 
mass of crystals, at the same time rising markedly in temperature. 
The amount of heat now liberated must enter the sodium acetate 
when the mass of crystals is melted again. 

The large amount of heat that must be liberated before 
water freezes accounts for the slowness of the formation 
of ice. It is also the reason why the temperature never 
falls so low in the vicinity of large lakes as it does far 
inland, the heat given out by the freezing water warming 
the surrounding air. 

The heat that disappears on melting and reappears on 
solidifying is called the heat of fusion. It is sometimes 
called latent heat since the heat seems to become hidden 
or latent. It is now believed that the heat energy that dis- 
appears when a body melts has been transformed into the 
potential energy of partially separated molecules. The 
heat of fusion therefore represents the work done in chang- 
ing a solid to a liquid without a change of temperature. 

182. Melting of Crystalline and Amorphous Substances. 
If a piece of ice is placed in boiling hot water and then 
removed, the temperature of the unmelted ice is still 
oC. There is no known means of warming ice -under 



HEAT AND WORK 203 

atmospheric pressure above its melting point and main- 
taining its solid state. Ice being composed of ice crystals is 
called a crystalline body. All crystalline substances have 
fixed melting points. For example, ice always melts at 
oC. The melting points of some common crystalline 
substances are given below:" 

Melting Points of Some Crystalline Substances 

1. AJuminun 658 C. 

2. Cast iron 1200 C. 

3. Copper 1083 C. 

4. Ice o C. 

5. Lead 327 C. 

6. Mercury 39 C. 

7. Phenol (carbolic acid) . - . 43 C. 

8. Platinum ": 1755 C. 

9. Salt (sodium chloride) 795 C. 

10. Saltpeter (potassium nitrate) 340 C. 

11. Silver. 961 C. 

12. Sodium .hyposulphite (hypo) 47 C. 

13. Zinc 419 C. 

Non-crystalline or amorphous substances such as glass, 
tar, glue, etc., do not have well defined melting points 
as do crystalline bodies. When heated they gradually 
soften and become fluid. For this reason glass can be 
pressed and molded. 

183. Change of Volume During Solidification. The 
fact that ice floats and that it breaks bottles and pipes in 
which it freezes shows that water expands on freezing. 
How a substance may occupy more space when solid than 
when liquid, may be understood when we learn that ice 
consists of masses of star-shaped crystals. (See Fig. 151.) 
The formation of these crystals must leave unoccupied 
spaces between them in the ice. When liquefied, however, 
no spaces are left and the substance occupies less volume. 



204 



PHYSICS 



Most substances contract upon solidifying. Antimony 
and bismuth, however, expand on solidifying while iron 
changes little in volume. Only those bodies that expand, 
or else show little change of volume' on solidifying, can 
make sharp castings, for if they contract they will not 



^C^ 
pK^ 






Fig. 151. Ice crystals. 

completely fill the mold. For this reason gold and silver 
coins must be stamped and not cast. Type metal, an 
alloy of antimony and lead, expands on solidifying to form 
the sharp outlines of good type. Several important 

effects of the expansion 
of water when freezing 
should be noted, (a) 
Ice floats, (b) if it sank 
as soon as formed, lakes 
and rivers would i reeze 
solid, (c) freezing water 
is one of the active 
agents in the disinteg- 
ration of rocks. 
Since water expands on freezing, pressure would on com- 
pressing ice at oC, tend to turn it into water. Pressure 
does lower the melting point of ice, so that a little ice may 
melt when it is subjected to pressure. On removing the 
pressure the water freezes. This may be shown by placing 
a loop of fine piano wire (see Fig. 152) over a piece of ice 




Fig. 152. Melting ice by pressure. 



HEAT AND WORK 205 

supported so that a weight may be hung upon the wire. 
The wire will be found to gradually cut through the ice, the 
melted ice refreezing above the wire. 

Important Topics 

1. Specific heat. 

2. Heat of fusion of ice. 

3. Crystalline substances have fixed melting points. 

4. Expansion on freezing, importance. 

Exercises 

1. What are two advantages in the high heat of fusion of ice? 

2. What are two advantages in the expansion of water while freez- 
ing? ( 

3. How much heat will be required to melt 1000 g. of ice and warm 
the water to 2oC? 

4. How many grams of ice at oC. can be melted by 400 g. of water 
atS5C? 

5. What are two advantages of the high specific heat of water? 
Two disadvantages? 

6. If the specific heat of iron is 0.1125, how much ice at oC. can 
be melted by a 200-g. ball of iron heated to 3ooC? 

7. What is the temperature of a hot ball of iron weighing 80 g., 
if when placed on a piece of ice at oC. it melts 90 g. of ice? 

8. If 500 g. of copper at 4ooC. are placed into 3000 g. of water 
at ioC. what will be the resulting temperature? 

9. What weight of water at 9oC. will just melt 10 kg. of ice at 
oC? 

10. If the smooth dry surface of two pieces of ice are pressed to- 
gether for a short time the two pieces will be frozen into one 
piece. Explain. 

n. Tubs of hot water are sometimes placed in vegetable cellars to 
prevent the vegetables from freezing. Explain. 

12. How many B.t.u. are given out when 2 lbs. of water freeze? 

(2) Heat and Change of State 
184. Heat of Vaporization. In our study of evaporation 
in Art. 174 we considered the more rapidly moving or 
vibratpg molecules in the liquid escaping to the air above 



2o6 



PHYSICS 



and the slower moving molecules being left behind in the 
liquid; this means that a loss of heat will result upon 
evaporation, the liquid remaining becoming cooler as the 
process continues. Now just as a ball thrown up in the 
air loses its kinetic energy as it rises, and acquires energy 
of position or potential energy, so molecules escaping from 
a liquid lose a certain amount of kinetic energy or heat and 
acquire a corresponding amount of energy oj position or 











n s v v OS^^ 




^NX>B 
















































\\\ s \N s 
























\\\N S N S 
























X\\\ s \ 
























v\\ SsS \ 
























n|^^\\"\ 
























\k\\\ 
























\s\\ 
























>s s 
















































\ 

























Fig. 153. -The black cube in the upper corner represents one cubic 
inch of water. The entire cube represents the space occupied by the cubic 
inch of water in the form of steam. The reduced spaces at the bottom 
and sides show how much short the cube is of being one cubic foot. 
(American Radiator Co.) 

potential energy. Conversely, as the ball returns to the 
ground its potential energy is changed to kinetic energy. 
Similarly when vapor molecules return to the liquid condi- 
tion they lose their energy of position and acquire kinetic 
energy. In other words, when a liquid evaporates a cer- 
tain amount of heat disappears, or becomes latent and 
when the vapor condenses the heat reappears, or becomes 
sensible heat. The amount of heat that disappears when 
1 g. of a substance is vaporized is called the heat of vaporiza- 



HEAT AND WORK 207 

tion. In the case of water at its boiling point, 536 calories 
of heat disappear when 1 g. of water turns to vapor, and 
this same amount of heat reappears when the vapor 
condenses. 

The change of volume of water on turning to steam is 
shown in Fig. 153. 

185. The Boiling Point. The boiling temperature 
depends upon the pressure. The boiling point may be 
defined as the temperature at which bubbles of vapor are 
formed within the liquid. These bubble increase the 




Fig. 154.: Effect of pressure on the boiling point. 

surface at which evaporation can take place in the liquid, 
and the principal reason why rapid application of heat to 
a liquid does not raise its temperature above the boiling 
point is that as more heat is applied more bubbles form 
so that the increase of evaporating surface supplies a 
correspondingly greater surface for cooling. The varia- 
tion of the boiling temperature with changing pressure may 
be shown by partly filling a strong %-in. test-tube with 
water. Close the neck with a one-hole rubber stopper 
through which passes a glass tube to which is attached a 
soft rubber tube. (See Fig. 154.) Support the tube by 
a holder, heat the water and boil until all the air is driven 



2o8 



PHYSICS 



from the tube, then close the soft rubber tube with a 
pinch cock and hold the tube in an inverted position. On 
cooling the end of the tube above the water with cold water 
or snow, the vapor within is condensed and the pressure 
upon the water is reduced. Vigorous boiling begins at 
once. By condensing the vapor repeatedly the water may 
be made to boil at the room temperature. At the top of 
Mt. Blanc water boils at 84C. while in steam boilers at 
225 lbs. pressure to the square inch the boiling point is 
nearly 2ooC. 

186. Laws of Boiling. The following statements have 
been found by experiments to be true. 

1. Every liquid has its own boiling point which under 
the same conditions of pressure is always the same. 

2. The temperature of the boiling liquid remains at the 
boiling point until all the liquid is changed into vapor. 

3. The boiling point 
rises with increased 
pressure and falls if the 
pressure is diminished. 

4. A boiling liquid 
and the vapor formed 
from it have the same 
temperature. On cool- 
ing, a vapor will liquefy 
at the boiling point. 

5. The solution of 
solid substances in a liquid raises its boiling point, ad- 
ditional energy being needed to overcome the adhesion 
involved in the solution. The boiling point is also affected 
by the character of the vessel containing the liquid. In 
glass the boiling point is 10 1. 

187. Distillation of Water. Usually when solids are 
dissolved in liquids the vapor coming from the liquid con- 




Fig. 1 55 . Distilling apparatus. 



HEAT AND WORK 



209 



tains none of the dissolved solid. Thus by evaporating 
salt sea water, and collecting and condensing the vapor, 
pure water is obtained. Distillation is the process of 
boiling a liquid and condensing the vapor formed back 
again into a liquid. (See Fig. 155.) The liquid to be 
distilled is placed in vessel F and boiled. The vapor is 
conducted into the tube / which is surrounded by a larger 
tube containing cold 
water. The vapor is 
condensed on the cold 
walls of the tube. 
The resulting liquid 
is collected in the 
vessel R. Distillation 
is employed, for two 
purposes: (a) To re- 
move impurities from 
a liquid (water is puri- 
fied in this way), (b) 
Mixtures of different 
liquids having differ- 
ent boiling points may 
be separated by dis- 
tillation. The one 




Fig. 156. A vacuum pan. 



having the lower boiling point will be vaporized first. 
Thus a mixture of alcohol and water, on distillation 
yields a distillate having a much larger percentage of 
alcohol than at first. Repeating this process which is 
called fractional distillation yields alcohol of increasing 
strength of purity. Distilled liquor such as alcohol, 
brandy, and whisky are made by distilling fermented 
liquor, alcohol being made from fermented grains. 
Gasoline and kerosene are distilled from crude petroleum. 
Sometimes as in the production of sugar or evaporated 



11 



2IO PHYSICS 

milk the object is to remove the water by evaporation in 
order to obtain the solid material. Since the two sub- 
stances named are injured by heating, the syrup, or milk 
is evaporated under reduced pressure in a vacuum pan, 
that is in a boiler from which air and vapor are removed 
by an air pump. (See Fig. 156.) 

188. Artificial Cooling. The fact has been brought out 
that when a solid is melted, a certain amount of heat, 
called the heat of fusion, is absorbed or disappears. This 
absorption of heat is also noticed when a solid is liquefied 
by dissolving it in a liquid as well as when it is liquefied 
by simply applying heat. Thus if some table salt is 
placed in a tumbler of water the temperature of the solu- 
tion is lowered several degrees below that of the salt and 
water used. The liquefaction or solution of the salt has 
been accompanied by an absorption or disappearance of 
heat. This heat has been taken from the salt and from 
the water, resulting in a lowered temperature. Sal am- 
moniac or ammonium nitrate when dissolved in water 
produce a much more marked cooling effect than does 
table salt. The dissolving of a crystal in a liquid is some- 
thing like evaporation, except that the molecules of the 
liquid attract the molecules of the solid and thus assist 
the change of state. 

189. Freezing Mixtures. If one attempts to freeze a 
solution of salt and water, ice will not form at oC. but 
several degrees lower. The ice formed however is pure. 
Evidently the attraction of the molecules of salt for the 
water molecules prevented the formation of ice until the 
motions of the 1 water molecules had been reduced more 
than is necessary in pure water. As the temperature of 
freezing water is that of melting ice, ice in a salt solution 
melts at lower temperature than in pure water. In a 
saturated salt solution this temperature is 2 2C. It 



HEAT AND WORK 



211 



is for this reason that the mixture of ice and salt used in 
freezing cream is so effective, the salt water in melting 
the ice, being cooled to a temperature many degrees below 
the freezing point of the cream. The best proportion 
for a freezing mixture of salt and ice is one part salt to 
three parts of finely powdered or shaved ice. 

190. Refrigeration by Evaporation. Intense cold is 
also produced by permitting the rapid evaporation of 
liquids under pressure. Carbon dioxide under high pres- 
sure is a liquid, but when allowed to escape into the air 



I Cold Storage 
Room 




Fig. 157. Diagram of a refrigerating system. 

evaporates so rapidly that a portion of the liquid is frozen 
into solid carbon dioxide which has a temperature of 8o 
C. The evaporation of liquid ammonia by permitting 
it to escape into a pipe, under reduced pressure, is used on 
a large scale as a means of producing cold in cold storage 
and refrigeration plants. (See Fig. 157.) 

The essential parts of the refrigerating system em- 
ploying ammonia is represented in Fig. 157. The com- 
pressor exhausts ammonia gas from the coiled pipe in 
" E" and compresses the gas in "C," where under 150 
pounds pressure and the cooling effect of water it con- 
denses to liquid ammonia. This is allowed to pass 
slowly through the regulating valve, whereupon it 



212 PHYSICS 

evaporates and expands in the long coiled pipe in "" 
on its way back to the compressor. This evaporation 
and expansion causes a large amount of heat to be 
absorbed from the brine, cooling the latter below the 
freezing point of pure water and thus permitting 
the freezing of cans of water suspended in the brine. 
The chilled brine may also be sent through pipes in 
order to cool storage rooms containing meat or other 
food products. The ammonia absorbs heat when it 
vaporizes and gives up heat when it is compressed and 
liquified. 

Important Topics 

1. Heat of vaporization, of water 536 calories per gram. 

2. Boiling point, effect of pressure upon boiling point, laws of 
boiling. 

3. Distillation, artificial cooling, freezing mixtures, refrigeration by 
evaporation. 

Exercises 

1. How much heat is required (a) to melt 1 g. of ice at oC, (b) 
to raise the temperature of the water resulting to iooC, (c) 
to change this water to steam? 

2. If the water leaving a steam radiator is as hot as the steam 
how is the room warmed? 

3. What is the effect of placing salt upon icy sidewalks in cold 
weather? 

4. Is rain water distilled water? Is it perfectly pure? 

5. What are two advantages of the high heat of vaporization of 
water? 

6. If the heat from 1 g. of steam at iooC. in changing to water 
and cooling to oC. could be used in melting ice at oC. how 
much ice would be melted? 

(3) Heat and Work 

191. Necessity for Heat Energy. From early times 
man has been able to transform motion into heat, and has 
used this ability in many directions as in starting fires and 



HEAT AND WORK 213 

warming himself by friction. It took man many centu- 
ries, however, to devise an effective machine for trans- 
forming heat into mechanical energy or to use it in doing 
work. 

The power of a man is small and as long as the work of 
the world had to be done by man power, progress was 
retarded. When man began the use of beasts of burden, 
he took a long step in advance since one man could then 
employ and direct the power of many men in the animals 
he controlled. Man also built water-wheels and windmills 
thus gaining power directly from the forces of nature and 
these added much to his working ability. But he took 
the greatest step in gaining control over his surroundings 
when he learned to use heat energy and to make it drive 
his machines. 

192. Heat Engines. At the present time there is a 
great variety of heat engines in use such as steam, hot air, 
gas, and gasoline engines, all using heat energy to produce 
motion. The expansive power of steam when confined 
has been observed for hundreds of years and many differ- 
ent machines have been invented to use it in doing work. 

193. The Steam-engine. The man who perfected the 
steam-engine, and devised its modern form was James 
Watt (1736-1819). The essential parts and the action 
of the steam engine may be readily understood by studying 
a diagram. In Fig. 158, S stands for steam chest, C for 
cylinder, P for piston and v for slide valve. The first two 
are - hollow iron boxes, the latter are parts that slide back 
and forth within them. The action of the steam engine is 
as follows: Steam under pressure enters the steam chest, 
passes into the cylinder and pushes the piston to the other 
end. The slide valve is moved to its position in Fig- 159. 
Steam now enters the right end of the cylinder, driving 
the piston to the left, the "dead" steam in the left end of 



214 



PHYSICS 



the cylinder escaping at E to the air. The slide valve is 
now shifted to its first position and the process is repeated. 
It will assist the student to understand this action if he 
makes a cardboard model of these parts, the piston and 




Fig. 158. Cross-section view of 
cylinder and steam chest of a steam 
engine. 



Fig. 159. The. steam drives 
the piston to the left. 



slide valve being movable. In practical steam-engines, 
the piston rod is attached to a crank rod fastened to a crank 
which turns a wheel. (See Fig. 160.) The back and 
forth, or reciprocating motion of the piston is by this means 



H" Steam Pfpe 
D^wfJ^K Thrott/e 




ExAaustPipe 

Fig. 160. External view of steam engine. 

transformed into rotary motion, just as in the sewing- 
machine the back-and-forth motion of the treadle produces 
rotary motion of the large wheel. Upon the shaft of the 
steam engine is fastened an eccentric (see Fig. 163) which 



HEAT AND WORK 



215 



moves the slide valve. The steam engine acts continu- 
ously as long as steam is supplied to it. Since it shifts the 

position of the slide 







I 



valve automatically, 
g-|1 it is called an auto- 
matic steam engine. 
, And because the 
5 * J3 K - steam drives the pis- 
9 8 -a ton both ways, it is 
called a double-acting 
steam engine. See 
Fig. 161 for a length- 
section of a modern 
locomotive. 

194. The Me- 



-o Z.X o 

uoot! 

^ - 
<o 3ft^ 

& y i> 

3 Oi* 

O M o, 

T^s- chanical Equivalent 
tfctjlj of Heat. While 
2 um watching workmen 
bore holes in cannon, 
Count Rumford, 
1753-1814, noticed 
with much interest 



2 e > 

rt A 



3 
pO > 

g^ g * the large amount of 

a y heat produced in the 

n process. 

-5 I " served that the heat 

^ t>x> 3 



He ob- 



g-3 % developed seemed to 
-, <3 have some relation to 
m( rt .- tne wor ^ done upon 
," I the drill in boring the 
Later experi- 
ments performed by 
many men indicated that a definite relation exists be- 
tween the heat produced by friction and the amount 



^ll* 1 



2l6 



PHYSICS 




of work done in overcoming the friction. This discovery 
indicates that in some way heat is related to energy 
and that heat is probably a form of energy. Later 
experiments have confirmed this idea, and it is now con- 
sidered well established that heat is a form of energy. 
Many attempts have been made to discover the relation 
between the units of heat energy and the units of mechan- 
ical energy. To illustrate one method employed, suppose 

one measures a given 
length in inches and in 
centimeters; on divid- 
ing one result by the 
other, it will be found 
that a certain relation 
exists between the two 
sets of measurements, 
and that in every case 
that i in. equals 2.54 
cm. Similarly, when 
the same amount of energy is measured both in heat 
units and in work units a constant relation is always 
found between the units employed. One B.T.U. is found 
equivalent to 778 ft. -lbs. 1, calorie being equivalent to 42,700 
g. cm. (427 g. m). This relation is called the mechanical 
equivalent of heat, or in other words it represents the 
number of work units equivalent to one heat unit. 

One of the first successful experiments in determining the 
relation between work units and heat units was devised 
by Joule in England. (See portrait p. 217.) The experi- 
ment consisted in taking a can of metal containing water 
(Fig. 162) in which was placed a thermometer, and a rod 
carrying paddles. The rod was turned by a cord con- 
nected through suitable apparatus to heavy weights, 
W and W. The energy represented by the downward 



Fig. 162. Apparatus for determining 
the mechanical equivalent of heat. 



William Gilbert (1540-1603), 
"Father of magnetic philosophy." 
Especially noted for his experi- 
ments and discoveries in magne- 
tism; first to use the word "electric- 
ity." First man to practically 
emphasize experimental science. 




Dr. William Gilbert 
(Popular Science Monthly) 




James Prescott Joule (181S- 
1889), England, determined the 
mechanical equivalent of heat; dis- 
covered the relation between an 
electric current and the heat pro- 
duced; first proved experimentally 
the identity of various forms of 
energy. 



James Prescott Joule 
(Popular Science Monthly) 



HEAT AND WORK 219 

motion of the weights through a given distance was com- 
pared with the heat energy developed in the water as 
shown by its rise in temperature. Careful experiments 
showed that when 778 ft.-lbs. of work had been done 
by the moving weights the heat produced at the same 
time would warm one pound of water 1 Fahrenheit 
degree. If the experiment was performed using metric' 
units, it was found that the expenditure of 42,700 gram 
centimeters (427 gram meters) would result in producing 
enough heat to warm one gram of water one centigrade 
degree. The facts just given may be summarized as 
follows: 778 foot-pounds of energy are equivalent to 1 British 
thermal unit and 42,700 gram centimeters, or 427 gram meters, 
of energy are equivalent to i calorie. This relation of work 
units to heat units is called the mechanical equivalent of 
heat. 

195. The Heat Equivalent of Fuels and Efficiency 
Tests of Engines. To determine the efficiency of a steam 
engine it is necessary to know not only the mechanical 
equivalent of heat but also the heat produced by burning 
coal or gas; 1 lb. of average soft coal should produce about 
12,600 B.t.u. Now since 778 ft.-lbs. are equivalent to 
one B.t.u. the energy produced when 2 lbs. of average soft 
coal is burned is 778 X 12,600 X 2 = 19,605,600 ft.-lbs. 
In actual practice 2 lbs. of average soft coal burned will 
develop about 1 horse-power for 1 hour. 1 horse-power- 
hour = 33,000 ft.-lbs. X 60 = 1,980,000 ft.-lbs. Noweffi- 

, work out 1,980,000 1 

ciency equals - 7. ~ z = or 10 per cent. 

work in 19,605,600 10 ^ 

This is the efficiency of a good steam engine. Ordinary 

ones require 3 lbs. of coal burned to each horse-power-hour 

produced or they are but % as efficient or have but about 

7 per cent, efficiency. 



220 



PHYSICS 



Heat of Combustion of Various Fuels 
Data in this table are taken from U. S. Geological Survey, Bulletin, 
No. 332, and U. S. Bureau of Mines, Bulletin No. 23. 



Calories 
per gram 




Alcohol, denatured 

Coal, anthracite, average. 
Coal, bituminous, average 

Gasoline 

Illuminating gas 

Kerosene 



11,600 

13,500 
12,600 

IQ,OCO 
l8,000 
19,900 



^,450 

7,500 

7,000 

10,550 

I0,000 

II,050 



Constants for Heat Transmission 

Data from "Ideal Fitter," American Radiator Co. 

B.t.u. transmitted per square foot per hour per degree 
(Fahrenheit) difference in temperature between inside 
and outside air. 

Brick Work 
4 in. thick = 0.68 
8 in. thick = 0.46 
12 in. thick = 0.33 



concrete 
cement 



50 per cent, more than brick. 



stone 33 H P er cent, more than brick. 



Window 1.090 [ 

Wood as wall = 0.220 j 
Double window = 0.560 [ 



concrete 
reinforced 



20 per cent, more than 
brick. 



Important Topics 

1. Heat a manifestation of energy. 

2. Steam-engine and its action. 

3. Mechanical equivalent of heat and heat equivalent of fuels 
and efficiency of engines. 

Exercises 

1. Construct a working model of the cylinder and steam chest of 
a steam engine and be prepared to explain its action. 

2. At $5.00 per ton how many B.T.U.'s should be produced from 
1 cent's worth of bituminous coal? 



HEAT AND WORK 221 

3. Try the following experiment: Place a quart of water in a tea- 
kettle and place it over the fire for 5 minutes, and note the rise 
in temperature and compute the number of B.T.U.'s entering 
the water. Place another quart of water at the same tempera- 
ture in an aluminum or tin dish and heat for 5 minutes, note 
the rise in temperature and compute the heat used before. 
Which of the dishes shows the greater efficiency? How do 
the efficiencies of the two dishes compare? How do you account 
for any differences in the efficiencies found? 

4. How high would 8 cu. ft. of water be lifted if all of the energy 
produced by burning 1 lb. of coal were used in raising it? 

5. What is the mechanical equivalent of a pound of coal expressed 
in horse-power hours? 

6. If a furnace burns 100 lbs. of coal a day and its efficiency is 
50 per cent, how many B.T.U.'s are used in warming the house? 

7. How many B.T.U.'s can be obtained by burning J ton of 
bituminous coal? 

8 When a pound of water is heated from 40F. to 2 1 2F., how many 
foot-pounds of energy are absorbed by the water? 

9. How many loads of coal each weighing 2 tons, could be lifted 
12 ft. by the energy put into the water in problem 8? 




Fig. 163. An eccentric. 

10. When 3 cu. ft. of water are used for a hot bath and the water 
has been heated from soF. to ii2F., how many B.T.U.'s 
have been absorbed by the water? 

11. If the average temperature of water at the surface of Lake 
Michigan is 5oF., how many B.T.U.'s would be given off 
by each cubic foot of water at the surface, if the tempera- 
ture of the water should drop 5F.? 

12. In a cold storage plant carbon dioxide gas is used. The pipe 



222 



PHYSICS 



13 



14 



leading from the compression pump to the expansion valve passes 
through a condensing tank of cold water. Why? 
When the gas is compressed in a cold storage plant, what be- 
comes of the energy used by the compression pump? 
An eccentric (Fig. 163), is a round disc mounted a little to one 
side of its center, A, on the engine shaft B. A band, C, on the 
circumference of the disc is connected by a rod, D, with the 
slide valve in the steam chest. How is the rotary motion of 
the shaft changed into a backward and forward motion of the 
slide valve? 

(4) Heat Engines 

196. The Gas Engine. One of the heat engines in 
common use to-day is the gasoline engine. It is used to 
propel automobiles and motor boats, to drive machinery, 



nd Valves 




Tighten Connecting Rod Ee^rings 



Drain Oil & 
Clean Strainer 



Fig. 164 Cut away view of a modern automobile engine, with parts 
requiring attention most frequently, indicated. (Courtesy of the 
"Automobile Journal.") 

etc. The construction and action of- a gasoline engine 
may be understood by studying a working model, or by 
proper diagrams. 

The common gasoline or gas engine is called a four-cycle 
(better four-part cycle) engine (see Fig. 164), since it re- 



HEAT AND WORK 



223 



quires four movements of the piston to complete one cycle 
or series of changes. This is illustrated in Fig. 165 I, which 
represents a cross-section of the cylinder of the gasoline 
engine with the piston moving downward. At the upper 
end of the cylinder are two ports or openings. One, the 
exhaust port, is closed, the 
inlet port is open and a mix- 
ture 01 gas and air is enter- / 
ing. Fig. 165 2 shows the 
piston returning; both ports 
are closed and the "charge" 
of air and gas is being com- 
pressed. As the piston 
reaches the end of its stroke 
in compressing the charge, an 
electric spark explodes or 
"fires" the charge of gas and 
air. The hot burning gas 
expands suddenly driving the 
piston downward with great 
force (Fig. 165 3). The pis- 
ton rod is attached to the 
crank of a heavy fly-wheel 
and this is given sufficient 
energy or momentum to keep 
it going through the next three strokes. Fig. 165 4 rep- 
resents the returning piston pushing out the burnt 
"charge" through the open exhaust valve e. On the next 
downward motion of the piston the valve e closes. It 
opens, and new charges of gas and air enter and the 
"cycle" is repeated. 

In order to make the motion more even and continuous 
and also to secure more power, more than one cylinder is 
attached to the same shaft and fly-wheel. Two, three, 




Fig. 



165. The four strokes of a 
gas engine cycle. 



224 PHYSICS 

four, six, eight and even more cylinders have been attached 
to one shaft. Four or six cylinders are commonly used in 
automobile gasoline motors. To lessen the sound of the 
"exhaust," the latter is sent through a "muffler" which 
often reduces the noise to a low throbbing. (See- Fig. 166.) 
The gasoline engine is more efficient than the steam-engine, 
since the fuel, gas, is burned in the cylinder and not in a 
separate furnace. The combustion of the fuel in the cylin- 
ders makes some special cooling device necessary to pre- 
vent their overheating. This usually consists of a casing 
about the cylinders. Between the cylinder and this 




Fig. i 66. An efficient automobile muffler. (Courtesy Popular Science 

Monthly.) 

casing is water which on being heated passes to a tank or 
radiator. In the radiator the water cools and then re- 
turns to the space between the cylinders and casing thus 
keeping up the circulation. 

197. Efficiency of Gas Engines. One may test the 
efficiency of a gas engine by determining the amount of 
power developed and comparing it with the mechanical 
equivalent of the fuel burned. Illuminating gas is some- 
times employed to drive gas engines. One cubic foot of 
illuminating gas should produce 600 B.T.U. when burned. 
The efficiency of the gas or gasoline engines is sometimes 
as high as 25 per cent. This engine is free from smoke 
and is also compact and quickly started. While the fuel, 
gas or gasoline, is somewhat expensive it is light and easily 



HEAT AND WORK 



225 



carried. Suppose a gas engine produces 1 horse-power 
and uses 20 cu. ft. of 
gas an hour, what is its 
efficiency? 1 horse- 
power-hour = 550 X 60 
X 60 = 1,980.000 ft. -lbs. 
20 cu. ft. of gas = 20 
X 600 X 778 = 9,336, 
000 ft. -lbs. 

. work in _ 

Efficiency = ; = 

J work out 

1,980,000 



21.2 



per 



9,336,000 
cent. 
198. Steam Turbine. 

One form of the steam- 




Fig. 167. The principle of the steam 
turbine. 



engine that is com- 
ing into general use 
is the turbine. (See 
Fig. 167.) This con- 
sists of a shaft to which 
are attached blades, the 
shaft and blades being 
contained in a closed 
case. Steam is admitted 
by nozzles and strikes 
the blades so as to set 
them and the shaft in 
motion. There are also 
stationary blades (see 
Fig. 168), which assist 
in directing the steam 

Fig. 168. Path of steam in DeLaval P ff pr1 -j V plv po-ain^r trip 
steam turbine, (a) and (c) movable enectively against tUe 

blades, (b) stationary. rotating parts. The 

15 




2 26 PHYSICS 

steam turbine is used for large power plants. (See Fig. 
293.) It is very efficient, makes very little vibration, and 
occupies about one-tenth the floor space that a reciprocat- 
ing engine of equal power uses. Some large ocean 
steamers are now driven by steam turbines. 

Important Topics 

1. The gas engine, its construction, action and efficiency. 

2. The steam turbine. 

Exercises 

1. If coal costs $4.00 a ton, and gas, $0.80 per 1000 cu. ft. what 
amounts of heat can be secured from 1 cent's worth of each? 

2. What will it cost to heat 30 gallons of water (1 gal. of water 
weighs about d>% lbs.) from 4oF. to iqoF. with coal cost- 
ing $4.00 per ton and yielding 12,000 B.T.U. per lb. if the heater 
has an efficiency of 50 per cent. 

3. What will it cost to heat 30 gallons of water from 4oF. to 
iqoF. with gas at $0.80 per 1000 cu. ft. if the heating device 
has an efficiency of 75 per cent. 

4. Construct a cardboard working-model showing the action of the 
gas engine and be prepared to explain the action of the various 
parts. 

5. If 500 lbs. of iron should fall 2000 ft. and all of the resulting 
mechanical kinetic energy should be transformed into heat, 
what would be the amount of heat produced? 

6. What are the special advantages of (a) the gasoline engine? 
(b) the turbine? (c) of the reciprocating steam engine? 

7. Do you burn coal or gas in your kitchen stove at home? Which 
is for you the more economical? Why? 

8. What are the advantages of using a tireless cooker? 

9. What is the efficiency of a locomotive that burns 3.2 lbs. of coal 
per horse-power-hour? 

io. A gas engine developed in a test 0.34 horse-power for 1 minute, 
and 50 seconds, 0.5 cu. ft. of gas being used. The heat of com- 
bustion of the gas was 600 B.T.U. per cu. ft. Find the 
efficiency of the engine. 

11. Find the horse-power of an engine, the diameter of the piston 
being 19 in., stroke 26 in.; it uses steam at an average pressure 
of 200 lbs. per square- inch and makes 100 strokes a minute. 



HEAT AND WORK 22 7 

12. What is the efficiency of an engine and boiler that develops 
200 horse-power, while burning 390 lbs. of soft coal per hour? 

13. If a locomotive has an efficiency of 6 per cent, and develops 
1700 horse-power how much coal is burned in an hour? 

14. If an automobile engine burns 1 gallon of gasoline in an hour and 
develops 10 horse-power, what is its efficiency? 

N B 2 

15. The A.L.A.M. 1 formula for horse-power is , when the pis- 
ton speed is 1000 ft. per minute, N being the number of cylinders 
and B, their diameter. Find the horse-power of a 4-cylinder 
engine, the cylinders having a diameter of 4 in. 

16. Find the horse-power of a 6-cylinder automobile engine, if the 
cylinder diameter is 4.5 in. 

17. A 4-cylinder automobile having 4-in. cylinders, uses 1 gallon of 
gasoline in 1 hour. Find its efficiency, if its average horse- 
power developed is 6. 

18. The motor boat Disturber III, has 24 cylinders each with diame- 
ter 3.5 in. If the piston speed is 1000 ft. per minute, what is 
the horse-power? (See problem 15.) 

Review Outline: Heat 

Heat; sources (4), effects (5), units (2). 

Temperature; thermometer scales (3), absolute temperature, 
oCY5 + 32 - F. 

Expansion; gases, Law of Charles (V1/V2 = T1/T2), liquids, 
peculiarity of water, solids, coefficient of expansion, uses, results. 

Heat Transference; conduction, uses of good and poor conduc- 
tors, convection, in nature, heating and ventilating systems, 
radiation, 3 peculiarities, value of sun's radiation. 

Heat and Moisture; relative humidity, dew point, formation of 
dew, fog, rain, snow, etc., evaporation, effects, conditions. 

Heat Measurement; specific heat, heat of fusion, of vaporization, 
combustion. 

Vaporization; Boiling point, laws of boiling, distillation, artificial 
cooling. 

Heat Engines; steam, gas, construction, action, efficiency, me- 
chanical equivalent of heat. Heat equivalent of fuels. 

1 American League of Automobile Manufacturers. 



CHAPTER IX 

MAGNETISM 

(i) General Properties of Magnets 

199. Magnets. Since the times of the early Greek 
philosophers men have known of certain stones that have 
the property of attracting to themselves objects of iron 
and steel. Such stones are called natural magnets. It is 
thought by many that the name magnet is derived from 
Magnesia in Asia Minor, where these stones are abundant, 
though this is but tradition. 

It was also learned long ago that iron and steel objects 
when rubbed with natural magnets be- 
come magnetized, that is, acquire the 
properties of magnets. These are said to 
be artificial magnets. 

Some 800 years ago it was discovered 
that magnets, natural or artificial, when 




Fig. 169. A bar magnet. 



Fig. 170. A horse- 
shoe magnet. 



suspended so as to turn freely, always come to rest in a 
definite position pointing approximately north or south. 
This is especially noticeable when the magnet is long 
and narrow. Because of this property of indicating 
direction, natural magnets were given the name of lode- 
stone (lode-leading). 
Artificial magnets are made by rubbing steel bars with a 

. 228 



MAGNETISM 



22Q 



N\A 



-~^-~ 



A. 



-Bar 
with 



magnet or by placing the steel bar in a coil of wire through 
which a current of electricity is flowing. The magnetized 
steel bars may have any form, usually they are either 
straight or bent into a "U" shape. These forms are 
known as bar and horseshoe magnets. (See Figs. 169 and 
1 70.) Magnets retain their strength best 
when provided with soft-iron "keepers," 
as in Fig. 171. 

200. Magnetic Poles. If a magnet 
is placed in iron filings and removed, 
the filings will be found to cling strongly 
at places near 4:he ends of the magnet, 
but for a portion of its length near the 
middle no attraction is found. (See 
Fig. 172.) These places of greatest 
attraction on a magnet are called poles. 
If a bar magnet is suspended so as to 
swing freely about a vertical axis the 
magnetic pole at the end pointing north is called the 
north-seeking pole; at the other end, is the south-seeking 
pole. In most places the needle does not point to the true 
north, but somewhat to the east or west of north. The 
direction taken by a magnetic needle is parallel to the 

magnetic meridian. 

201. Law of Magnetic Ac- 
tion. The north pole of a 

Fig. 172. Iron filings attracted to magnet is usually marked, 
the poles of a magnet. T . , - , , . 

If a marked bar magnet be 
held in the hand and its north-seeking pole be brought near 
the north-seeking pole of a freely suspended bar magnet, 
the two poles will be found to repel each other, as will also 
two south-seeking poles, while a north-seeking and a south- 
seeking pole attract each other. (See Fig. 173.) Th!s 
action leads to the statement of the Law of Magnetic 



Fig. 171. 
magnets 
keepers. 



23 



PHYSICS 



Action: Like poles repel, while unlike poles attract each 
other. The force of attraction or repulsion lessens as the 
distance increases. The force of the action between magnetic 
poles is inversely proportional to the square of the distance 
between them. Compare this with the law of gravitation 
(Art. 88). 

202. Magnetic Substances and Properties. It is found 
that if an iron or steel magnet is heated red hot that its 
magnetic properties disappear. Accordingly one method 
of demagnetizing a magnet is to raise it to a red heat. If 





Fig. 173. Like poles of two 
magnets repel. 



Fig. 174. A magnetoscope. 



a magnet that has been heated red hot and then cooled is 
brought near a suspended bar magnet, it is found to 
attract either end, showing that it has regained magnetic 
properties even though it has lost its magnetic polarity. 
A suspended bar magnet used to test the magnetic proper- 
ties of a body is called a magnetoscope. (See Fig. 174.) 
The needle of a magnetic compass serves very well as a 
magnetoscope. Magnetic properties are most strongly 
exhibited by iron and steel, though nickel and cobalt show 
some magnetic effects. There is a peculiar alloy of copper, 
aluminum, and manganese, known as Heusler's Alloy, that 
is also magnetic. However, of all substances, iron and 
steel show the strongest magnetic effects. 



MAGNETISM 23 1 

203. Magnetic Induction. Let the north-seeking pole of 
a bar magnet support an iron nail by its head. (See Fig. 
175.) Test the point of the nail for polarity. Seewhether 
a second nail can be attached by its head to the point of the 
first. Test the polarity of the point of this nail. Find by 
trial how many nails can be suspended in succession from 
the magnet. Test in each case for polarity. Withdraw 
carefully the magnet from the first nail the string of 
nails will fall apart. Repeat the test with a thickness of 
paper between the magnet and the first nail. 

Results similar to those secured at first will 
be found, though probably fewer nails will 
be supported. The presence of paper be- 
tween the magnet and nails simply weakens 
the action. Test the action of the magnet 
upon the nail when there is between them a 
piece of glass, one's thumb, thin pieces of 
wood, copper, zinc, etc. The magnetizing 
of a piece of iron or steel by a magnet near or 
touching it is called magnetic induction. This , p? 

action takes place through all substances FlG x _ 
except large bodies of iron or steel hence Nails magne- 
these substances are often used as magnetic auction. 
screens. The pole of the new induced magnet 
adjacent to the bar magnet is just opposite to the pole 
used. Thus the N.-pole of the magnet used will produce 
a S.-pole at the near end of the nail and a N.-pole at 
the end farther away. (See Fig. 175.) On removing the 
magnet, the nails are found to retain a part of their in- 
duced magnetism. 

204. Retentivity. In several of the foregoing para- 
graphs it has been seen that a piece of iron or steel when 
once magnetized does not entirely lose its magnetism when 
the magnetizing force is removed. Different pieces of 



N 

'S 

N 

s 



232 PHYSICS 

iron and steel vary greatly in this respect, some remaining 
strongly magnetized, others losing much of their magnet- 
ism. This property of retaining magnetism is called reten- 
tivity. Hardened steel has a high degree of retentivity, 
while soft iron retains but little magnetism. 

Important Topics 

i. Magnet; natural, artificial, bar, horseshoe. 

2. Magnetic poles; north seeking, south seeking. 

3. Law of action, magnetoscope, retentivity, induced magnet. 

Exercises 

1. Make a summary of the facts of magnetism presented in this 
lesson. 

2. Is magnetism matter, force, or energy? How do you decide? 
To what other phenomenon that we have studied is it similar? 
How? 

3. Make a simple magnetoscope for yourself by suspending a thin 
steel needle or rod 5 to 10 cm. long, with a light thread or silk 
fiber at its center, so that it will hang level. Then magnetize 
the needle, and keep the magnetoscope in your book. 

4. Name three uses for magnets or magnetism. 

5. Mention three uses for a magnetoscope. 

6. Are all magnets produced by induction? Explain. 

7. In what magnetic devices is a high retentivity desirable? 

(2) The Theory of Magnetism and Magnetic Fields 

205. The Theory of Magnetism. If a magnetized 
watch spring is broken in two, each part is found to be a 
magnet. If one of these parts be broken and this process 
of breaking be continued as far as possible, the smallest 
part obtained has two poles and is in fact a complete 
magnet. (See Fig. 1,76.) It is supposed that if the divi- 
sion could be continued far enough that each of the mole- 
cules of the steel spring would be found to have two poles 



MAGNETISM 



233 



N 



1 

2 
3 



N 



St. 



S N 

3 C 



S N 

mm 

S N 
3 & 



I! 



m 

N S 



Fig. 176. Effect of breaking a magnet. 



and to be a magnet. In other words, magnetism is be- 
lieved to be molecular. Other evidence supporting this 
idea is found in the fact that when a magnet is heated red 
hot, to a temperature of violent molecular motion, its 
magnetism disap- 
pears. Also if a 
long, fine soft iron 
wire be strongly- 
magnetized, a 
light jar causes its 
magnetism to dis- 
appear. This would lead us to believe that magnetism 
is not a property of the surface of the body, but that it 
depends upon molecular structure or the arrangement 
of the molecules. 

It is believed 
also that the mol- 
ecules of a mag- 
netic substance are 
magnets at al 
times; that before 
the body is magnetized the molecules are arranged 
haphazard (see Fig. 177) but that when a magnet is 
brought near, the molecules tend to arrange themselves 
in line, with their 
nor th-s e eking 
poles pointing in 
the same direction. 
(See Fig. 178.) If 
the magnet is 



<f %CB 


<?<^>um<X(^g 


S>^> 


BD^)^ 


BD^ \ 


%^ fl ^C^^XBSjBE 


i&% 


<?&><? 


|W 


4>%mL 


^>P<^^>iSS>i 


Qb<? 


%<*% 


<^<^ 


%<?% 


<^ ^, mo c^om^> % 


zm<& 


B%^> 



Fig. 177. Possible arrangement of molecules 
in an unmagnetized iron bar. 



WD TOD wri linn win nun bihti nun mnn nun imin mnn imrn nun man win iniii i 
HID TOD TOD BID HUD HD (ED HID CUD imh ann ninn nnn mn nMI Ifflin IDIO 
urn win imri win nnp~i |wn qrcin nun mnn mnn mm~i nrnnmnn nmn nmnmirn irmn 

bd hd bud un qbd an ud dud mn md mo hhp qsd diid hid no (hud 



Fig. 178. Arrangement of molecules in a 
saturated magnet. 



jarred some of the molecules tend to get out of line, perhaps 
to form little closed chains of molecules. (See Fig. 177.) 
206. Magnetic Fields and Lines of Force. The be- 
havior of magnets is better understood after observing and 



234 PHYSICS 

studying the lines of force of a magnet. The earliest 
descriptions of these are by William Gilbert, the first 
Englishman to appreciate fully the value of making 
experimental observations. He wrote a book in 1600 
called De Magnete in which he published his experiments 
and discoveries in magnetism. (See p. 217.) 

Magnetic lines of force may be observed by placing a 
magnet upon the table, then laying upon it a sheet of paper 
and sprinkling over the latter fine iron filings. On gently 
tapping the paper, the filings arrange themselves along 




Fig. 179. Iron filings on paper over a bar magnet 

curved lines extending from one end of the magnet to 
the other. These are called the magnetic lines of force. 
(See Fig. 179.) The space about a magnet in which the 
magnetic lines are found is called the magnetic field. (See 
Fig. 180.) 4 

Many interesting things have been discovered concern- 
ing the lines of force. Some of the facts of magnetic action 
are given a simple explanation if we think of them as due 
to the magnetic lines of force. A summary' of several 
discoveries concerning magnetic fields follows: 



MAGNETISM 



235 



(A) Magnetic lines of force run side by side and do not 
cross one another. (See magnetic fields.) 

(B) Magnetic lines of force are believed to form'" closed 
curves " or to be continuous. The part outside of the mag- 
net is a continuation of the 
part within the magnet. (See 
Fig. 180.} 

(C) The attraction of a 
magnet is strongest where the 
magnetic lines are thickest, 
hence they are believed to be 
the means by which a magnet FlG- x 80 Diagram of the field 

attracts. of a bar magnet. 

:e like poles repel and unlike poles attract, it 
hat the action along a line of force y 
th directions It has therefore beenf 





. Magnetic field between like poles showing 

to indicate by an arrow head (Fig 
hat a north-seeking pole tends to mc 
:e. The lines of force are considered 
seeking pole of a magnet and entering 
>le. (See Figs. 181 and 182.) 



236 



PHYSICS 



(E) A freely suspended small magnet in a magnetic field 
places itself parallel to the lines of force. (Test this by 
holding a magnetic compass in different portions of a 
magnetic field). Note the position of the needle and the 
lines of force. This fact indicates that the compass needle 
points north on account of its tendency to turn so as to be 
parallel to the earth's magnetic field. 

(F) Each magnet is accompanied by its own magnetic 
field. When a piece of iron is brought within the field 




Fig. 182. Magnetic field between unlike poles showing attraction. 

of a magnet the lines of force passing through the iron 
tend to arrange the iron molecules in line or to magnetize 
the iron. 

207. Magnetic Induction. The action of magnetic 
lines of force in magnetizing iron when they pass through 
it, is called Magnetic Induction. This may now be defined 
as the production of magnetism in a body by placing it 
within a magnetic field. Freely suspended magnets place 
themselves parallel to the lines of force in a magnetic 
field, therefore when an iron rod is placed in a weak field, 
or one with few lines of force, the iron is but slightly 
magnetized; that is, but few molecules are brought into 




J 



MAGNETISM 237 

line. Increasing the strength of the magnetizing field, 
gives stronger magnetization to the iron up to a certain 
point. After this, stronger fields give no increase in 
magnetizing effect. When iron exhibits its greatest 
magnetization it is said to be saturated. 

208. Permeability. If a piece of iron is placed between 
the poles of a horseshoe magnet, the "field" obtained by 
sprinkling iron filings upon a sheet of paper over the 
magnet resembles that shown in Fig. 
183. The lines in the space between 
the poles of the magnet seem to 
crowd in to the piece of iron. The 
property of the iron by which it tends 
to concentrate and increase the num- 
ber of lines of force of a magnetic 
field is called permeability. Soft iron 

shows high permeability. Marked _ ,.- _ i _ 

. , . . , Fig. 183. Effect 

differences in behavior are shown of a piece of iron in 
by different kinds of iron and steel a ma s netic field - 
when placed in a magnetic field. Very pure iron, or soft 
iron, is strongly magnetized by a magnetic field of medium 
strength. Its magnetism, however, is quickly lost when 
the magnetizing field "is removed. This indicates that 
soft-iron molecules are easily swung into line, but also 
disarrange themselves as easily when removed from a 
magnetizing force. Soft-iron magnets having high per- 
meability quickly lose their magnetism. They are there- 
fore called temporary magnets. On the other hand a 
hardened steel bar is difficult to magnetize, but when once 
magnetized retains its magnetism permanently, unless 
some action weakens the magnet. Such magnets are 
called permanent magnets. 

Note. The term "line of force" as used in this text means the 
same as 'line of induction" as used in more advanced texts. 



238 PHYSICS 

Important Topics 

1. Molecular theory of magnetism, saturation, permeability. 

2. Magnetic fields and lines of force. 

3. Six facts concerning magnetic fields. 

Exercises 

1. Name an object whose usefulness depends upon its retentivity. 
Explain. 

2. How do you explain the rententivity of hard steel? 

3. Are the molecules of a piece of iron magnetized at all times? 
Explain. 

4. When a piece of iron is magnetized by induction does any 
magnetism enter the iron from the magnet? Does the magnet 
lose as the iron gains magnetism? Explain. 

5. Have all magnets been produced by induction? Explain. 

6. Why will tapping a piece of iron when in a magnetic field increase 
the amount it will be magnetized? 

7. Express in your own words the theory of magnetism. 

8. Place two bar magnets in a line 5 cm. apart, unlike poles ad- 
jacent; obtain the magnetic field with iron filings. Sketch it. 

9. Repeat Exercise No. 8 using like poles. Describe the appear- 
ance of a field that gives attraction; of a field that gives repulsion. 

(3) The Earth's Magnetism 

209. The Earth's Magnetic Field. Dr. William Gil- 
bert's famous book, De Magnete, contains many helpful 
and suggestive ideas, none perhaps more important than 
his explanation of the behavior of the compass needle. He 
assumed that the earth is a magnet, with a south-seeking 
pole near the geographical north pole, and with a north- 
seeking pole near the geographical south pole. This idea 
has since been shown to be correct. The north magnetic 
(or south-seeking) pole was found in 1831, by Sir James 
Ross in Boothia Felix, Canada. Its approximate present 
location as determined by Captain Amundsen in 1905 is 



MAGNETISM 



239 




240 PHYSICS 

latitude 70 5' N. and longitude 96 46' W. The south 
magnetic pole is in latitude 72 S., longitude 155 16' E. 
The north magnetic pole is continually changing its posi- 
tion. At present it is moving slowly westward. 

210. Direction of the Earth's Magnetic Field. Ref- 
erence has been made to the fact that the compass does 
not always point exactly north. This indicates that the 
earth's magnetic field varies in its direction. Columbus 
discovered this fact upon his first voyage. The discovery 
alarmed the sailors since they feared they might come to 
a place where the compass would be unreliable. This 
variation is called declination. It is defined as the angle 
between the direction of the needle and the geographical 
meridian. Declination is due to the fact that the geo- 
graphical and magnetic poles do not coincide. What is 
meant by a declination of 90 ? Lines drawn upon a map 
so as to pass through places of the same declination are 
called isogonic lines. The line passing through points 
where the needle points north, without declination, is 
the agonic line. The agonic line is slowly moving west- 
ward. It now passes near Lansing, Michigan; Cincinnati, 
Ohio; and Charleston, S. Carolina. (See Fig. 184.) At 
all points in the United States and Canada east of the 
agonic line the declination is west, at points west of the 
agonic line the declination is east. 

21 1. The Dipping Needle. Mount an unmagnetized 
steel needle on a horizontal axis so as to be in neutral 
equilibrium, that is, so as to remain balanced in any posi- 
tion in which it is left. Upon being magnetized and 
placed so that it can swing in a north and south plane, 
the north-seeking pole will now be found to be depressed, 
the needle forming an angle of nearly 70 with the hori- 
zontal. (See Fig. 185.) The position assumed by the 
needle indicates that the earth's magnetic field instead of 



MAGNETISM 



241 




Fig. 



being horizontal in the United States dips down at an angle 
of about 70 . Over the magnetic pole, the dipping needle 
as it is called, is vertical. At the earth's equator it is 
nearly horizontal. The angle between a horizontal plane 
and the ear til's magnetic lines of force 
is called the inclination or dip. 

212. Inductive Effect of the 
Earth's Magnetic Field. The 
earth's magnetic lines of force are 
to be considered as rilling the space 
above the earth, passing through 
all objects on the surface and into 
and through the earth's interior. 
The direction of the earth's field is 
shown by the compass and the 
dipping needle. Magnetic lines of 
force tend to crowd into and follow iron and steel objects 
on account of their permeability. Therefore, iron or 
steel objects, such as posts, columns, etc., are permeated 
by the earth's lines of force, which in the United States 
enter at the top of these objects and leave at the bottom. 
The lines of force passing through these bodies arrange 
their molecules in line or magnetize the bodies. The 
inductive effect of the earth's magnetism indicates how 
lodestones or natural magnets acquire their magnetized 
condition. So far as is known, magnetism produces no 
effect upon the human body. It can therefore be studied 
only by observing its effects upon magnets or bodies 
affected by it. 



185. A dipping 
needle. 



Important Topics 

The earth's magnetic field, dip, declination, agonic line, induction 
by the earth's field. 



16 



242 PHYSICS 



Exercises 



1. How would a dipping needle be of assistance in locating the 
magnetic poles of the earth? 

2. Will a dipping needle weigh more before or after it is mag- 
netized? Explain. 

3. It is said that induction precedes attraction. Using this idea, 
explain how a magnet attracts a piece of soft iron. 

4. Devise an experiment to show that a piece of iron attracts a 
magnet just as a magnet attracts a piece of iron. 

5. Give two methods for determining the poles of a magnet. 

6. State three of the most important points in the theory of mag- 
netism. What evidence supports each? 

7. Why is a permanent magnet injured when it is dropped? 

8. Name two important uses of the earth's magnetic field. 

9. What magnetic pole would you find at the top of an iron post 
that has stood for some time in the ground? What pole at the 
bottom? How would you test this? 



CHAPTER X 
STATIC ELECTRICITY 

(i) Electrification and Electrical Charges 

213. Electrical Charges. The ideas gained in the study 
of magnetism are of assistance in the study of electricity 
in giving some fundamental ideas and principles that will 
often be referred to as a basis for comparing the actions 
of magnetized and electrified bodies. The process of 
electrifying a body is very different from that of magnet- 
izing it. Thus if a rubber comb or rod be rubbed with a 
woolen cloth the object rubbed is able to attract to itself 
light bits of paper, thread, etc. This peculiar attraction 
was noticed and recorded by the ancient Greeks, 600 B. C, 
when it was found that amber when rubbed wou'd attract 
light objects to itself. For a long time it was supposed 
that amber was the only substance showing this property. 
Dr. William Gilbert, however, discovered that the elec- 
trified condition could be produced by rubbing a great 
variety of substances. He named the result produced, 
electrification, after the Greek name for amber (elektron). 
A body like hard rubber or amber which will attract light 
objects when rubbed is said to be electrified, or to have 
been given a charge of electricity. 

214. Law of Electric Action. Let a vulcanite rod be 
electrified by rubbing with a woolen cloth until it will 
attract light objects; then place it in a wire stirrup 
suspended by a silk thread. If a second vulcanite rod is 
similarly electrified and brought near the first, the two 

243 



244 



PHYSICS 




will be found to repel. (See Fig. 186.) If now a glass red 

be rubbed with silk and brought near the suspended rod, 

the two will attract. This difference in behavior indicates 

a difference in the electrification or charge upon the rods. 

The two charged vulcanite rods repelling and the charged 

glass and vulcanite attracting indicate 

the law of electric action. Like charges 

repel each other and unlike charges attract 

each other. Extensive experiments with 

all kinds of substances indicate that 

there are but two kinds of electrical 

charges. The electrical charge upon 

glass when rubbed with silk or wool is 

called positive, and that upon hard rubber or vulcanite 

when rubbed with wool is called negative. 
215. The Electroscope and its Uses. An electroscope 
is a device employed to test the pres- 
ence of an electrical charge. The 
aluminum foil electroscope consists of a 
flask closed by a rubber stopper 
through which passes a rod which ends 
at the top in a ball or plate and below 
is attached two narrow leaves of thin 
aluminum-foil. Ordinarily the two 



Fig. 186. Repulsion 
of like charges. 




Fig. 187. An aluminum 
foil electroscope. 



Fig. 188. A proof plane. 



leaves hang close together and parallel but if a charged 
body is brought near the electroscope the leaves 
spread apart at the bottom. (See Fig. 187.) The 
kind of charge upon a body may be determined with an 
electroscope as follows: Make a proof -plane by sealing a 



STATIC ELECTRICITY 245 

small metal disc on the end of a hard rubber rod. (See 
Fig. 188.) Touch the disc of the proof -plane first to a 
charged rubber rod and then to the top of the electroscope. 
The leaves of the latter will separate showing that the 
electroscope is charged. This charge remains after the 
proof-plane is removed. If the charged vulcanite rod is 
brought near the electroscope, the leaves separate further 
That is, a charge like that on the electroscope makes the 
leaves separate further. But if an unlike charge, as that 
on a positively charged glass rod, is cautiously brought 
near, the leaves will be seen to move together. 

216. Two Charges are Produced at the Same Time. 
A closely fitting woolen cover or cap some 3 in. long is 
made for the end of a vulcanite rod. A silk thread at- 
tached to the cap enables one 
to hold the latter while the a= 
rod is turned within it. (See 
Fig. 189.) If the rod bear- Fig. 189. Rod with woolen cap. 
ing the cap is held near a 

charged electroscope little or no effect is noticed. If 
now the cap is removed by the silk thread and held near 
the electroscope, it will be found to be positively charged 
while the rod is negatively charged. The fact that no 
result is seen when the cap and rod are together, indicates 
that one charge neutralizes the other. In other words, 
the charges must be equal. This illustrates the truth that 
when electrification is produced by friction, the two objects 
rubbed together acquire equal and opposite charges. 

217. Charging by Contact and Conduction. If a small 
pith ball is suspended by a silk thread, a charged rod 
brought near is at first attracted, but after contact is 
repelled (see Fig. 190) showing that the ball has become 
charged with the same kind of electrification that is upon 
the rod. That is, a charge given to an object by contact 




246 PHYSICS 

with a charged body is of the same kind as that upon the 
charged one. The proof -plane in Art. 215 carries the 
same kind of charge that is upon the rod it is charged from. 
Some substances have the ability to transfer charges of 
electrification. These are called conductors, those that 
do not conduct electrification are insulators. The con- 
ducting power of a body is readily 
tested by placing one end of a rod 
of the material upon the top of an 
electroscope and the other end upon 
an insulated support, as in Fig. 191. 
If now a charge be put in contact 





Fig. 190. The pith ball Fig. 191. Testing for conductivity, 
charged by contact is re- 
pelled. 

with the body of a, the electroscope will show by its leaves 
whether the rod tested conducts or not. The leaves sepa- 
rate instantly when conducting substances are tested, 
while no action results with insulators. In testing some 
materials for conductivity the leaves are found to diverge 
gradually. Such bodies are said to be poor conductors. 
All degrees of conductivity are found. The metals are 
the best conductors. The best insulators are rubber, 
mica, shellac, glass, silk, porcelain, parrafin, and oils. 

Important Topics 

1. Positive and negative changes. Law of electric action. 

2. Electroscope and its uses. 

3. Conductors and insulators. 



STATIC ELECTRICITY 



247 



Exercises 

1. Is air a conductor? Give reasons for your answer. 

2. Mention two points of likeness and two points of difference 
between magnetism and electrification. 

3. If you were testing the electrification of a body with a charged 
pith ball suspended by a silk thread, would attraction or repul- 
sion be the better test? Give reasons. 

4. Have you ever produced electrification by friction outside of a 
laboratory? Explain. 

5. Are the rods upon which we produce electrification by friction, 
conductors or insulators? How do you explain this? 

6. Are conductors or insulators of the greater importance in prac- 
tical electricity? Explain. 



(2) Electric Fields and Electrostatic Induction 

218. Electrical Fields. In our study of magnetism we 
learned that a magnet affects objects about it by its mag- 
netic lines of force. In a similar 
way it is assumed that a charged 
body produces electrical effects 
upon its surroundings by electric 
lines 0] force. For example, 




h- 



Fig. 192. An electric field about 
a positively charged shell. 



Fig. 193. A "detector." 



the attraction that a charged body exerts upon light objects 
through short distances or the influence of a charge upon an 
electroscope several feet away, is said to be due to the electric 
field about the charged body. (See Fig. 192.) The pres- 
ence of the electric lines of force may be shown by placing 
a perforated, slender, diamond-shaped piece of tissue 
paper upon a light glass pointer (Fig. 193). When placed 



248 



PHYSICS 




Fig. 194. 



-Electric field between unlike 
charges. 



in an electric field the tissue paper "detector" places itself 
parallel to the lines of force. Electric lines of force are 
said to extend from a positive to a negative charge. (See 
Fig. 194.) The direction shown by the arrow upon the 

lines is that along which 
a small positive charge 
tends to move. Electric 
lines of force unlike 
those from magnets are 
not continuous. They 
extend from a positive 
charge to a negative 
charge. Therefore each 
positive charge is connected by lines of force to a negative 
charge somewhere. These ideas of electric fields are of 
mugh assistance in explaining many electrical effects. 
Electrical fields between oppositely charged shells will be 
found similar to Fig. 194, while between shells with like 
charges, fields are found as in Fig. 195. 

219. Electrostatic In- 
duction. If a charged 
body is brought near 
an aluminum-foil elec- 
troscope, the leaves 
separate. (See Fig. 
198.) The nearer the 
charge is brought the 
wider the leaves spread, 
but when the charge is removed, the leaves collapse show- 
ing that nothing was given to the electroscope. It was 
simply affected by the charge in its vicinity. This pro- 
duction of an electrified condition in a body by the influence 
of a charge near it is called electrostatic induction. Placing 
insulators, such as a sheet of glass, between the charge 




Fig. 195. 



-Electric field between like 
charges. 



STATIC ELECTRICITY 



249 



and the electroscope does not affect the result, which is 
apparently brought about by the action of the electric 
lines of force. These lines of force extend without diffi- 
culty through uncharged insulators and terminate often at 
the surface of a conductor, where their influence causes 
a charge to accumulate. Charged insulators, however, do 
affect inductive action. This may be noticed by using a 
sensitive electroscope. 

220. Electrical Separation by Induction. The action 
just described may be illustrated further by taking two 
insulated, uncharged brass shells, A and B. (See Fig. 
196.) Bring a charged vulcanite rod near shell "A " 




Fig. 196. Production of two charges by 
the influence of a third charge. 




Fig. 197. The two 
charges separated. 



while the shells are touching each other. Then remove 
.shell B (Fig. 197) while tjie rod remains near A. On 
testing the shells for electrification, A is found to possess 
a positive charge. This action is in some respects similar 
to magnetic induction, for if one places a north-seeking 
pole near a piece of iron, the iron develops by induction a 
south-seeking pole at the end nearest the magnet and a 
north-seeking at the other end. There is, however, one 
striking difference. If the magnetized iron be separated 
into two parts, each part is a complete magnet possessing 
two unlike poles; while if the object affected by elec- 



250 



PHYSICS 



trostatic induction is separated into two parts one part 
has a positive charge and the other a negative charge. 

221. Charging a body by induction is easily accom- 
plished. To charge an aluminum-foil electroscope by 
induction bring near (say 10 cm.) from the top of the 
electroscope a charged rubber rod. (See Fig. 198.) 
The separated leaves show the presence of the repelled 
or negative charge, the positive charge being on the disc at 




- 1 1 \- 




m 




Fig. 198. Fig. 199. Fig. 200. 

Fig. 198. Effect of a charged rod near an electroscope. 
Fig. 199. When a finger is touched to the top of the electroscope, the 
repelled negative charge escapes. 

Fig. 200. The electroscope is now positively charged. 

the top. If while the charged rod is held near, the 
metal top of the electroscope is touched by the finger the 
leaves at once fall together showing that the repelled 
negative charge has escaped from the electroscope (Fig. 
199). On removing first the finger and next the charged 
rod, the positive charge spreads over the metal parts of 
the electroscope, as is shown by the separation of the 
leaves (Fig. 200). The electroscope is now charged posi- 
tively by induction. If the charged rubber rod is brought 
to about 30 cm. from the electroscope, its leaves tend to 



STATIC ELECTRICITY 25 1 

move together. If a body charged similarly to the elec- 
troscope or positively, is moved toward the electroscope the 
leaves separate further. This behavior of the electro- 
scope enables one to determine the kind of charge upon a 
body. 

Two principles of electrostatic induction may now be 
stated: (i) Two equal, unlike charges are always pro- 
duced by electrostatic induction. 

(2) If the body affected by induction is connected to 
the earth by a conductor, the repelled or "free" charge 
is conducted away from the body while the "bound" 
charge is held by the inducing charge. 

These principles apply in every case of induction. 

Important Topics 

1. Electric lines of force. Characteristics (3). 

2. Electrostatic induction. Principles (2). 

3. Charging by induction. Explanation. 

Exercises 

1. What are elctric lines of force? Where are they found? What 
does the arrow mean upon the lines? 

2. Name three effects produced by electric fields. 

3. Does electrostatic induction occur outside of laboratories? 
Where? When? 

4. Given a charged rubber rod, how may one charge from it by 
induction, insulated brass shells, giving some a positive and 
some a negative charge? 

5. How may the charges upon the shells be tested ? 

6. In charging an electroscope by induction, why must the finger 
be removed before the glass rod ? 

7. Why is it best to have the rubber and glass rods, used in elec- 
trification, warmer than the air of the room in which the ex- 
periments are being performed? 

8. When a sharp metallic point is held near the knob of a charged 
electroscope the leaves quickly come together. Explain. 



252 PHYSICS 

9. Might one of the members of your class in physics be charged 
with electricity, if he should stand on a board supported by dry 
glass insulators? Explain. 
10. If a metal can is charged strongly while standing on an insulator, 
tests made by means of the proof-plane and electroscope show 
no charge on the inside. Explain. 

(3) Electrical Theories and Distribution of Charges 

222. Franklin's Theory of Electricity. We have studied 
the production of electrification by friction and induction. 
It will be helpful now to consider some of the theories of 
electricity. From the ease with which electrification 
moves .along a conductor, many have imagined that elec- 
tricity is a fluid. Benjamin Franklin's One Fluid Theory 
held that a positive charge consisted in an accumulation 
or an excess of electricity while a negative charge implies 
a deficiency or less than the usual amount. This theory 
led to representing positive electrification by a plus (+) 
sign and negative, by a minus ( ) sign. These signs are 
in general use to-day. The use and significance of these 
signs should be clearly fixed in mind. 

223. The Electron Theory. Various discoveries and 
experiments made in recent years indicate, however, 
that negative electricity consists of little corpuscles or 
electrons which may pass readily from one molecule 
of a conductor to another while their movement through 
an insulator is much retarded if not entirely prevented. 
This theory, sometimes called the Electron Theory, holds 
that each atom of a substance has as a nucleus a corpuscle 
of positive electricity, and surrounding it, minute negative 
corpuscles or electrons. It is thought that the electrons 
in the atom are very much smaller than the positive 
charges and are revolving about the latter with great 
rapidity. Ordinarily, the positive and negative charges 
are equal so that the atom is in a neutral or uncharged 



STATIC ELECTRICirY 253 

condition. By the action of various forces some of the 
negative corpuscles within a conductor may be moved from 
molecule to molecule. Thus if a negatively charged rod 
is brought near a conductor, many electrons stream away 
to the far end charging it negatively, while the nearer end 
of the conductor is left with fewer electrons than usual 
along with the fixed positive corpuscles. Hence the near 
end is positively charged. (See Fig. 198.) On the other 
hand, if a positive charge is used, it attracts the electrons 
from the far end, leaving the immovable positive cor- 
puscles there, and that end becomes positively electrified, 
while the nearer end with its surplus of electrons is, of 
course, negatively electrified. 

The Electron Theory is considered well founded since 
the electrons have (a) had their mass determined, (b) 
their speed measured, (c) their electric charge determined, 
(d) and their behavior while passing through magnetic 
and electric fields observed. These facts and other 
experimental evidence have demonstrated the existence of 
electrons. The positive corpuscle has not been directly 
observed but is assumed to exist to account for the 
effects observed in induction, charging by friction, etc. 

224. Distribution of an Electric Charge upon a Con- 
ductor. We have applied the electron theory in explain- 
ing the phenomenon of electrostatic induction,. Let us 
now use it in studying the distribution of an electric charge 
upon a conductor. Let a cylindrical metal vessel open 
at the top and insulated by being placed upon pieces of 
sealing wax have a charge of negative electricity given 
it. (See Fig. 201.) On now taking a proof plane and 
attempting to obtain a charge from the interior of the 
vessel no result is found, while a charge is readily obtained 
from the outside of the dish. This result is explained by 
considering that the electrons are mutually self-repellant 



254 



PHYSICS 



and in their attempt to separate as widely as possible pass 

to the outer surface of the vessel. This same condition 

is also true of a dish made of woven wire. If the charged 

conductor is not spherical in outline, an uneven distribution 

of the charge is observed. Thus if an egg-shaped conductor 

. is insulated and charged (see Fig. 202), 

, a proof plane touched to the broad end 

JL of the body and then to an electroscope 

causes a certain divergence of the leaves 

of the latter. If now a charge be taken 

from the pointed end by the proof plane 

to the uncharged electroscope, a greater 

uh m spreading of the leaves than before will 

Fig 201 No ^ e n ticed. This indicates that the 

charge is found inside electricity may be unevenly distributed 

a hollow vessel. _ . . . 

over the surface of a body. It is found 
that the electric density, as it is called, is greatest where the 
surface curves most sharply. At a very sharp curve, as at 
a point, the electric density may be so great that a part 
of the charge escapes into the air. (See Fig. 203.) For 
this reason electric conductors on which it is desired to 
keep an electric charge have round surfaces 
and all sharp points and corners are avoided. 
While conductors, such as lightning rods, 
which are designed to facilitate the escape 
of electric charges, are provided with a num- 
ber of sharp points at the end or elsewhere. 
At such points, air particles are drawn More charge at 
forcibly against the point and after being ^ pointed 
charged are driven away strongly, creating 
the so-called electrical wind which carries away the charge 
at a rapid rate. (See Fig. 203.) 

225. Lightning and Electricity. The fact that light- 
ning is an electrical discharge was first shown in 1752 by 




Fig. 



STATIC ELECTRICITY 



255 



Benjamin Franklin, who drew electric charges from a cloud 
by flying a kite in a thunderstorm. With the electricity 
which passed down the kite string he performed a number 
of electrical experiments. This discovery made Franklin 
famous among scientific men everywhere. Franklin then 





Fig. 203. Electrical wind produced 
by a pointed conductor. 



Fig. 204. Electrical whirl. 
The reaction from the electri- 
cal wind causes it to revolve. 



suggested the use of lightning rods to protect buildings 
from lightning. These rods act as conductors for the 
electric discharge and thus prevent it from passing through 
the building, with the risk of overheating some part and 
setting the latter on fire. The 
points provided at the top of 
lightning rods are believed to aid 
in preventing strokes of lightning 
by the silent discharge of the so- 
called electric wind which tends 
to quietly unite the charges in the 
clouds and on the earth beneath. 

The charge in an electrified cloud 
acts inductively upon the earth 
beneath, attracting an opposite 
charge to the objects below. The 

discharge from the cloud often passes to the objects 
beneath, such as trees or buildings. Thunder is believed 
to be due to the sudden expansion of the air when intensely 




Fig. 205. The wire screen 
protects the electroscope. 



256 PHYSICS 

heated by the electric discharge and its sudden contraction, 
like a slap, as the track instantly cools. Thunder at a 
distance is usually followed by rumblings due to changes 
in the intensity of the sound mainly due to reflections of 
sound waves from clouds and other reflecting surfaces. 

226. An electric screen is a device for cutting off the 
influence of an electric charge. Faraday found that if a 
sensitive electroscope is surrounded by a wire mesh- screen 
(see Fig. 205), no evidence of electrification could be found 
inside. In other words, a network of conductors on a 
building makes the best protection against lightning, 
provided it is connected to the earth by good conductors 
at several places. 

Important Topics 

1. Electrical theories. Evidences for electron theory. 

2. How is the theory used in explaining induction? 

3. Charges, and distribution on conductors (effect of shape). 

4. Lightning: cause, effects, lightning rods. 

Exercises 

1. In what respects is Franklin's one-fluid theory like the electron 
theory? In what respects different ? 

2. Consider two shells charged by induction from an electrified 
rubber rod, one positively and one negatively. Explain the 
process, using the ideas of the electron theory. 

3. Should the metal top of an electroscope have sharp corners? 
Explain. 

4. Would a tall steel tower have the same need of a lightning rod 
as a brick chimney of the same height? Explain. 

5. Will a solid sphere hold a greater charge of electricity than a 
hollow one of the same diameter? Explain. 

6. If a positively charged cloud floats over a tree which is a good 
conductor of electricity will the tree be charged ? Show diagram. 
Explain. 



STATIC ELECTRICITY 



257 



(4) Potential, Capacity and the Electric 
Condenser 

227. Conditions Causing a Movement of Electricity. 

In the study of conductors and insulators it was observed 
that an electric charge moved along the conducting rod 
to the electroscope. This movement of electricity along a 
conductor is a result of great practical importance. We 
will now consider the conditions that produce the "flow" 
or "current" of electricity. 





Fig. 206. Electricity flows from 
high to low potential. 



m 
Let two electroscopes stand 

near each other. Charge 

one, C (Fig. 206), strongly 

and charge the other 

slightly. If now a light 

stiff wire attached to a 

stick of sealing wax be 

placed so as to connect the 

tops of the electroscopes, 

the leaves of C will partly 

close while those of D will 

open slightly, thus indicating a movement of electricity 

from C to D along the wire. The movement was from 

a place of greater degree of electrification to one of less. 

228. Potential. The potential of an electrified body is 

its degree of electrification. Therefore, it is said that 

electroscope C mentioned above has a greater potential 

than electroscope D. The movement of electricity is from 

a place of greater or high potential to one of lesser or low 

potential. If two bodies are at the same potential there 

will be found no movement of electricity between them. 

A difference of potential between two points connected by 

a conductor is therefore the necessary condition for an 

electric current. Just as heat is transmitted along a con- 

17 



2 5 8 



PHYSICS 



ductor from a place of high to one of lower temperature, so 
electricity is transmitted along a conductor from a place 
of high to one of low potential. Thus potential in elec- 
tricity corresponds to temperature in heat. One is the 
"degree of electrification," the other, "the degree of 
hotness." 

229. Electrical pressure is a term sometimes used for 
difference of potential. To better understand electrical 




Fig. 207. Air pressure apparatus to illustrate electrical pressure. 

pressure, consider three round tanks (Fig. 207) containing 
air. A is a tank holding air at 10 lbs. pressure per square 
inch, above atmospheric pressure, B is open to the air 
and hence is at atmospheric pressure while C has a partial 
vacuum, with 10 lbs. less pressure than that of the atmos- 
phere. If the valve at D or E is opened a flow of air sets 
up until the pressures are equalized. While if the pump 



STATIC ELECTRICITY 



259 



fl 



u 



at P is working a difference in pressure is easily maintained. 
Tank A corresponds to an insulated body charged to a high 
positive potential; tank B, open to the air, a body connected 
to the earth; while tank C represents a body having a 
negative potential. The earth is said to have zero potential. 

Now just as compressed air will be pushed into the 
atmosphere (as from A to B) while air p| 

at atmospheric pressure will if possible be H 

forced itself into a partial vacuum (as from 
B to C), so electricity at a positive potential 
will tend to move to a place at zero 
potential, while that at zero potential 
tends to move to a place of negative 
potential. Bodies at the same potential 
as the earth, or at zero potential, are also 
said to be neutral. Those positively 
electrified have a positive potential, 
those negatively electrified have a nega- 
tive potential. As in gases, movement 
always tends from higher pressure (poten- 
tial) to lower pressure (potential.) met d' plate gives 

230. 'Capacity. If we have a 100-gallon the electroscope a 

** greater surface 

tank and a 10-gallon tank connected by and hence greater 
a pipe both filled with compressed air, capacl y - 
the larger tank will contain ten times as much air as the 
smaller at the same pressure since it has ten times the 
capacity, or, if the two tanks are separated and the same 
amount of air is contained in each, the pressure of the 
air contained in the small tank will be ten times that in 
the large one. 

The electrical capacity of a conductor is in some respects 
similar to the capacity of a tank for air. Since, however, 
electrical charges are upon the surface of a body, its ca- 
pacity depends in part upon the extent of surface. For 




260 PHYSICS 

example, if a charge is taken from a charged rubber rod by a 
proof plane to an electroscope a certain divergence of the 
leaves will be noticed. If a circular metal plate several 
times the diameter of the top of the electroscope is laid 
upon the latter (see Fig. 208), and a charge equal to that 
used before is brought to the electroscope, the leaves show- 
less divergence than before, showing that the same charge 

__.__ ____ gives a lower potential 

I '-] when placed upon a body 



Fig. 209. A plate condenser. 



4- -4- -I- 4- -|- -|- -4- -{- ^ of greater capacity. 

231. The electric 
condenser is a device 
having a large electrical capcatiy consisting of parallel 
conductors separated by good insulators. It has been 
devised to enable one to obtain a large electrical charge 
upon a body of convenient size. Such an apparatus is 
of great practical value in many experiments and opera- 
tions. Its construction involves the principle of electro- 
static induction in which a charge of one kind attracts 
and "holds" strongly a 
charge of opposite kind e^ 

near it.-'- In its simplest 
form it consists of two 
parallel conductors sepa- 
rated from each other FlG - 2IO -~ A c p ^ t d e e s nser of several 
(Fig. 209). The upper 

plate has been charged negatively. This has given the 
lower plate a positive charge by induction, since the 
latter is connected to the earth. These positive and neg- 
ative charges hold or "bind" each other so that a 
large quantity may be accumulated. To increase the 
capacity of a condenser, several plates are used connected 
as in Fig. 210. 

It is a curious fact that the kind of insulator between the 



O- 



STATIC ELECTRICITY 261 

charged conductors of a condenser affects its capacity. 
Thus if glass, paraffine, or beeswax is between the plates 
instead of air, the plates will "hold" more electricity at 
the same potential. For this reason condenser plates 
are often separated by sheets of glass, paraffined paper, 
or mica. 

232. The Leyden Jar. A convenient form of con- 
denser, used as long- ago as 1745, is the Leyden jar. It 
consists of a glass jar (Fig. 211) coated part way up, 
inside and out, with tinfoil. The inner coating is con- 
nected by a chain to a knob at the 
top. The Leyden jar is charged by 
connecting the outer coating to the 
earth while to the inner coating is 
given a charge of either kind of 
electricity. The other kind of charge 
is developed by induction upon the 
outer coating, and each charge binds Fig. 211. A Leyden jar 
the other. To discharge a jar, a and a discharger, 
conductor, as a wire, is connected first to the outer coat- 
ing and held there while the other end is brought to the 
knob at the top. A bright spark is produced when the 
two charges combine. It is best not to let the discharge 
from the jar pass through the body unless one is certain 
that only a very small charge is present. 

233. Oscillatory Discharge. The discharge from a 
Leyden jar is an interesting phenomenon. The rush of 
electricity from one coat to the other does not stop when 
the two coats are exactly neutralized but continues until 
the two plates are charged just oppositely to their con- 
dition at first, then a rush of electricity in the opposite 
direction occurs. This alternation continues several 
times and constitutes what is called the oscillatory dis- 
charge. (See Fig. 414.) This oscillatory discharge sets 




262 PHYSICS 

up waves in the ether. These are called Hertzian waves 
in honor of their discoverer, Heinrich Hertz. They are 
the ether waves used in wireless telegraphy. A light- 
ning flash has been shown by photographs and by other 
means to be oscillatory. This fact supports the idea 
that the electrical conditions just preceding the stroke 
of lightning reproduce a condenser on a large scale. 
The charged cloud is the upper charged plate, the earth 
beneath, charged by induction from the cloud, is the lower 
charged plate, while the air between is the insulator or 
dielectric as it is sometimes called. 

Important Topics 

1. Potential: high, low, zero, positive, negative, similar to tem- 
perature and air pressure. 

2. Capacity affected by (1) area, (2) induction. 

3. Condensers, Leyden jar, parallel plate. 

4. Oscillatory discharge, conditions, results. 

Exercises 

1. Is the air a conductor? Explain. 

2. Can the Leyden jar be strongly charged if the outer coat is 
insulated? Explain. 

3. Upon what two conditions does the capacity of a body depend ? 
How in each case? 

4. Would a lightning discharge produce wireless waves? Explain. 

5. If a sharp tack be dropped point up on the plate of an electro- 
scope the latter is quickly discharged. Explain. 

(5) Electrostatic Generators 

234. Static Electric Machines. Many machines have 
been invented to produce larger quantities of static elec- 
tricity than we have used in the experiments previously 
described. One of the earlier of these was the plate fric- 
tion machine in which a large circular glass plate was 
rotated while a pad of some material was held against it. 
This machine was capable of producing powerful effects, 



STATIC ELECTRICITY 263 

but it took much work to turn it, and it has been aban- 
doned for a more efficient device, the static induction 
machine. 

235. The electrophorus is the simplest static induction 
generator, consisting 



1-- 



4-4-4-4-- 



simply of a flat circu- 
lar plate of some insu- 
lating material, as * ~ 

, Fig. 212. An electrophorus 

paramne, shellac, or 

rosin contained in a metal pan, and a flat circular metal 

disc having an insulating handle. 

The electrophorus is used as follows: The plate is first 
electrified by rubbing or beating with fur or a woolen 
cloth. The plate will be found to be charged negatively. 
The metal disc is placed upon the plate by holding the 
insulating handle. The upper surface of the charged body 
is slightly uneven so that the disc touches but a few high 
points. The greater part of the charged surface is sepa- 
n rated from the metal 

disc by air, a good in- 
sulator. The charge 
therefore acts induct- 
ively upon the disc 

repelling negative elec- 

1 ^ 1 m t 

1 ' tncity to the upper 

Fig. 213. Electrophorus charged. r - ,, .. 

surface of the disc, 

leaving the lower surface charged positively (Fig. 212). 
If now the finger is touched to the disc the repelled nega- 
tive charge escapes and the whole disc is left positively 
charged. The disc is now removed (Fig. 213) and the 
charge upon it may be tested or used in any desired man- 
ner. The disc may be recharged many times without 
rubbing the plate again. 

These electrical charges possess energy. What is the 



+ + H + -I- 

+ +" + + + + 



264 PHYSICS 

source of this energy? The answer may be determined 
by the following experiment. Place the disc upon the 
charged plate. Touch the disc with the finger to remove 
the repelled charge. Connect an electroscope to the disc 
by a fine wire. Nothing appears on the electroscope, 
since the disc has been connected to the earth, and is 
therefore at zero potential. If now the disc is lifted 
slowly, the leaves of the electroscope gradully separate, 
showing that a charge of electricity appears when the 
disc is being lifted against the force of attraction between 
the two charges. Just as potential energy is developed in 
a weight when it is lifted against the earth's attraction 
so electrical energy appears in the disc while it is being 
separated from the plate. The electrical energy of the 
charge is therefore due to the work done in separating the 
two charges. This electrical energy appears as heat and 
light, when the disc is discharged. It may be employed 
to ignite gas, gunpowder, etc. 

236. The Toepler-Holtz Induction Machine. This 
is a type of induction or influence machine that is often used 
for producing a continuous supply of electricity as in the 
operation of "X" ray machines, in lecture demonstrations, 
etc. This machine (Fig. 214) consists of two discs: one 
fixed, the other mounted so as to revolve. Upon the 
back of the fixed plate are two sectors of tinfoil which 
become charged oppositely. Upon the revolving plate 
are six metallic discs. These discs act like the discs of 
the electrophorus. They become charged by induction 
from the charges upon the sectors fastened to the fixed 
plate. The brushes held by a rod touch the discs at just 
t the right time to take off the repelled charge. The charges 
induced upon the discs are taken off by two metal combs 
whose points are held close to the revolving disc. The 
Leyden jars assist in accumulating a good strong charge 



STATIC ELECTRICITY 265 

before a spark passes between the terminal knobs. Some 
machines are built up of several pairs of plates and give 
correspondingly large amounts of electricity. 



Fig. 214. The Toepler-Holtz induction machine. 

Important Topics 

Static Electric Generators. (a) plate friction machine, (b) electro- 
phorus, (c) induction or influence machine. 

Exercises 

1. Potential is similar to what other terms that we have studied? 

2. What three electrical phenomena are better understood from a 
study of the lines of force? 

3. How many charges may be produced by an electrophorus before 
the plate needs to be electrified again? Explain. 

4. The static induction machine is often called a "continuous 
electrophorous." Why? 

5. The Leyden jars used with the induction machine cause much 
brighter sparks to be produced than without them. Explain. 

6. With the Leyden jar* removed, would the frequency with which 
the sparks pass between the knobs be increased or decreased? 
Explain. 

7. Mention three likenesses and three differences between magnet- 
ism and static electricity. 

8. Will you receive a greater shock by touching a knob of a charged 
Leyden jar when it is held in the hand or when it is standing on 
a sheet of glass? Explain. 

9. In what way may an electric charge be divided into three 
equal parts? 



266 



PHYSICS 



Review Outline : Magnetism and Static Electricity 



Comparison between Magnetism and Static Electricity. 
J magnetic, [ conductors, 

I non-magnetic. 1 insulators. 



Substances are: 



Produced by: 
Theory: 

Fields of Force 
Explain: 



Terms: 



Likeness: 
both are: 



Differences: 



induction, 
molecular, 
attraction, 
repulsion, 
induction, 
action of compass 
magnetoscope, dip 
declination, pole, 
retentivity, 
permeability, 
lodestone, 
magnetic meridian 



friction, or induction. 

electron, (fluid) 
I attraction, 
1 repulsion, 
I induction. 



electroscope, electron, 
positive, negative, 
potential, capacity, 
condenser, electrophorus, 
oscillatory discharge, 
I lightning. * 
a-produced by induction, 5-attract and repel, 
c-have fields of force, 
a-electricity can be conducted, magnetism 

cannot. 
6-electricity in all substances, magnetism in few. 
c-magnetism with the compass indicates 
direction. 



CHAPTER XI 
CURRENT ELECTRICITY 

(i) Electrical Currents and Circuits 

237. Sources of Electric Currents. In studying the 
production and distribution of static electricity it was 
seen that if two bodies at different potentials are connected 
by a copper wire a movement of electricity to the body having 
the lower potential occurred along the conducting wire. 
This movement of electricity is called an electric current 
(Art. 227). A difference of potential is therefore often 
called an electromotive force (E.M.F.), since it produces the 
movement of electricity in a conductor. The current 
between two oppositely charged bodies lasts for so short a 
time as to be of little or no practical value unless some 
means are found for continually recharging the bodies. 
That is, some device must be used to restore the difference 
in potential as fast as the conducting wire equalizes it. 
The continual charging of the bodies takes work. In 
other words, it requires a continual expenditure of some 
form of energy (which is converted into electrical energy) 
to produce the electric current. Two forms of energy are 
commonly used for this purpose. 

(A) Chemical energy is employed in voltaic cells for pro- 
ducing electric currents. (B) Mechanical energy is used 
for the same purpose in the dynamo and similar devices. 

238. The voltaic cell is named after Volta, an Italian 
physicist, who in 1800 invented it. In its simplest form 
it consists of a strip of copper and a strip of zinc placed in 
dilute sulphuric acid (one part acid to fifteen or twenty 

267 



268 



PHYSICS 



of water) (Fig. 215). By the use of sensitive apparatus, 
it can be shown that the copper plate of the voltaic cell 
has a positive charge and the zinc plate a negative charge. 
For example, let a flat plate 10 cm. in diameter be placed 
upon the knob of an electroscope and a similar plate, 
coated with shellac and provided with an insulating handle, 
be set upon it to form a condenser. (See Fig. 216.) If 
now wires from the two plates of a simple voltaic cell be 
respectively connected to the plates of the condenser, 



tZ 




Fig. 215 . Cross-sec- 
tion of a simple voltaic 
cell. 



Fig. 216. Testing the charges upon 
the plates of a simple voltaic cell. 



charges from the copper and zinc plates will accumulate 
upon the two condenser plates. Now remove the wires 
and lift the upper plate. The " bound" charge upon 
the lower plate will spread over the leaves and cause them 
to separate. Upon testing, the charge from the zinc plate 
will be found to be negative and that from the copper plate, 
positive. Since a positive charge is found upon the 
copper plate it is called the positive electrode; the zinc 
plate is called the negative electrode. 

239. Test for an Electric Current. If the copper and 
zinc plates of a voltaic cell are connected by a wire, a 



CURRENT ELECTRICITY 269 

current of electricity is set up in the conductor. Evidence 
of the current may be obtained by holding the conducting 
wire over and parallel to the needle of a magnetoscope. 
The needle is deflected by the action of the current parallel 
to it (Fig. 217). This magnetic effect of a current is the 
means usually employed for the detection and measurement 
of an electric current. Such 
a device which detects an 
electric current by its mag- 
netic effect is called a galvano- 
scope, in honor of Galvani, 
who in 1786 was the first to 

Hkrnvpr rinw tn rrnr1iirp an FlG - 217. The magnetic needle is 
discover now to produce an deflected by the current. 

electric current. 

240. The Electric Circuit. The entire conducting path 
along which a current of electricity flows is called an electric 
circuit. In the case of a voltaic cell, the circuit includes 
not only the wires connecting the plates but also the plates 
themselves and the liquid between them. When some 
device or apparatus is to receive current from the cell, 
it is attached to the plates and wires so that the device 
is a part of the electric circuit. Separating the circuit 

at any point is called break- 




"" q / ^ w__,.J ing or opening the circuit, 

P i#Si while connecting the ends of 

- S ~ B . an open circuit is called mak- 

FiG. 218. Diagram of an electric . ,.-. . * 

bell circuit. m g or closing the circuit. A 

device for opening and closing 
a circuit is called a key or switch. The electric circuit used 
in ringing a door bell is familiar to most boys and girls. 
This circuit is open most of the time. It is closed by 
pressing ' the push-button at the door, and the flow of 
current through the electric bell causes the latter to ring. 
Such a circuit is represented in Fig. 218. Here C is the 



270 PHYSICS 

voltaic cell, the two lines representing the plates of the 
cell. A cross-section view of the push-button (P), shows 
how the circuit is closed, (B) is the bell. Wherever cur- 
rent electricity is used the device in which it is employed 
forms a part of an electric circuit extending back to some 
electric generator. This generator must be able to 
continually produce an E.M.F., or a difference of potential 
between its terminals, in order that the movement of 
electricity may be continuous. 

Important Topics 

(a) Electric generators: (1) voltaic cell uses chemical energy; (2) 
dynamo uses mechanical energy. 

(b) Electric circuits: (1) open, (2) closed, (3) key and switch. 

(c) Voltaic and galvanic electricity (names). 

(d) Galvanoscope, uses. 

Exercises 

1. In what two ways are static and current electricity alike? In 
what two different? 

2. Draw a diagram of an electric bell circuit at your home. Give 
the location of the electric bell, the electric generator and the 
push-button. Show the connecting wires, and explain briefly 
how the circuit is operated. 

3. Represent some other electric circuit, naming the generator and 

other devices in the circuit. 

4. Look up the work of Volta and Galvani and write a statement of 
the electrical discoveries and inventions made by them. 

(2) The Voltaic Cell and its Action 

241. The simple voltaic cell consists of a strip of copper 
and a strip of zinc placed in dilute sulphuric acid. (See 
Fig. 219.) A short time after placing the plates in the 
acid, bubbles of a gas (hydrogen) appear on the surface 
of the zinc. These bubbles increase in size and some rise 
to the surface of the liquid. Nothing appears upon the 



CURRENT ELECTRICITY 



271 



copper plate. If the tops of the plates are connected by a 
wire, an electric current is set up through the wire and the 
cell, and bubbles of gas also appear upon the copper as 
well as on the zinc. In a short time the surface of the 
copper becomes coated with bubbles and the current be- 
comes much weaker. If the plates are left in the acid for 
some time the zinc is found to be eaten away, having been 
dissolved in the acid through 
chemical action. The copper, 
however, remains practically 
unaffected. 

242. How the Current is 
Produced. To maintain the 
electric current a continual 
supply of energy is required. 
This is furnished by the chem- 
ical action of the acid upon the 
zinc. The chemical action 
is in several respects like com- 
bustion or burning, by means 
of which chemical energy is 
transformed into heat energy. In the voltaic cell the 
chemical action of the acid upon the zinc transforms 
chemical energy into electrical energy. The E.M.F. 
or difference of potential may be considered as originating 
at the surface of the zinc where the chemical action takes 
place. At this point the zinc has the lower and the liquid 
in contact with it the higher potential. The molecules 
of the acid are believed to be separated or broken up into 
two parts called ions; one ion, the SO4 or sulphion, com- 
bines with the zinc forming zinc sulphate, the other, or 
hydrogen (H) ion, passes over to the copper plate, and 
accumulates on the surface of this plate giving it a posi- 
tive charge. It is therefore called the positive ion. 




Fig. 219. A simple voltaic cell. 



272 



PHYSICS 



Cu 



V 



P 



Zn 



The sulphion ion, or SO4 ion, carries a negative charge to 
the zinc. It is therefore called the negative ion. 

243. The Direction of the Current.* Beginning at the 
surface of the zinc the direction of the movement of posi- 
tive electricity may be traced through the liquid to the 
copper plate, to the wire, to the zinc plate, to the starting 
point, thus completing the electric circuit. When the 
circuit is closed it is found that the movement of electricity 
starts in all parts of the circuit at practically the same instant. 

244. The production of the current may be illustrated 
by describing a device for producing a continuous circu- 
lation of water. Thus let Cu 
and Zn represent two pipes 
connected by two horizontal 
tubes, one at V provided 
with a valve and one at P 
with a rotary Pump. (See 
Fig. 220.) Suppose the pipes 
filled to the level of V and the 
pump started. The pump 
will force water from Zn to 
Cu, through P, the level fall- 
ing in Zn and rising in Cu. 

If the valve V is open the water will flow back through 
V as long as the pump is working. If V is closed, the level 
in Cu will rise as high as the driving force of the pump can 
send it. If now V is opened, the pump will maintain the 
water in circulation from Cu to Zn through V. In the 
illustration, the tubes Cu and Zn correspond to the con- 
ducting plates of copper and zinc of a voltaic cell. The 
pump P represents the chemical action which produces 

* Many scientists consider that current in a conductor consists of 
negative electrons flowing in a direction ' opposite to that described in 
Art. 243. This is called the electron current, as distinguished from the 
electric current described above. 






Fig. 220. A comparison of 
a voltaic cell and circuit to a 
water pump and connecting 
pipes. 



CURRENT ELECTRICITY 273 

the electrical pressure. The upper pipe represents the 
part of the circuit outside of the cell, the valve V corre- 
sponds to an electric key or switch which is used to open 
and close the electric circuit. 

245. Polarization. In the simple voltaic cell, after the 
circuit is closed, bubbles of hydrogen collect upon the 
copper plate. This accumulation of hydrogen gas is 
called polarization. It acts as a non-conducting layer 
upon the surface of the plate and seriously interferes 
with the movement of electricity from the liquid to the 
copper plate not only in the simple voltaic cell but in 
many others as well. Some voltaic cells are made en- 
tirely free from this defect, either (a) by the removal of 
the hydrogen as fast as it is formed, or (b) by the use of 
such chemicals that no hydrogen is produced. 

246. Local Action. It is noticed that when a strip of 

zinc is placed in dilute acid that bubbles appear upon the 

surface of the zinc. The appearance of these agm 

bubbles indicates that some of the hydrogen ions y|||j 

carrying positive electricity have moved to the 

zinc plate. Careful examination of the plate after 

it has been in acid shows numerous black spots 

upon it. These are bits of carbon. They are 

always found in ordinary zinc. Small electric cur- 

J J Fig. 221. 

sents are set up which run from molecules of pure Local 
zinc into the liquid and back to the carbon particles, actlon - 
thus forming small closed circuits. (See Fig. 221.) The 
formation of these circuits from and to the zinc is called 
local action. This action is a defect in voltaic cells since 
a' part of the current is thus kept from passing through 
the main outside jcircuit, and the zinc may be consumed 
even when no outside current is flowing. 

247. Amalgamation. Local action is prevented by coat- 
ing the zinc with mercury. This process is called amalga- 
mation. The mercury covers the entire surface of the 



1 



> 



18 



274 PHYSICS 

plate in the acid. Its action is to dissolve pure zinc and 
bring it to the outer surface where it is acted upon by the 
acid. The carbon particles are kept covered so that no 
local currents can be formed as long as the bits of carbon 
are below the surface. Amalgamation therefore prevents 
local action. 

Important Topics 
The Simple Voltaic Cell 

i. Two plates: zinc, copper; electrolyte, dilute sulphuric acid. 

2. Ions: hydrogen, positive: sulphion, negative. 

3. Current, where and how produced, direction, illustration. 

4. Polarization: cure, local action, cure. 

Exercises 

1. Write in your own words an account of the production of an 

electric current by the simple voltaic cell. Use sketches. 

2. Which plate has the higher potential? How is it produced? 

3. Would you expect to get an E.M.F. by forming a cell of two 
copper plates? Why? 

(3) Practical Voltaic Cells 

248. Advantages of Voltaic Cells. Many forms of vol- 
taic cells have been devised. Several of the more com- 
mon of these will be described and their electro-chemical 
action explained. 

At the present time voltaic cells are employed only where 
small currents are needed, such as for electric bells and 
induction coils. Where more than a small amount of 
current is required, the dynamo and the storage battery 
have generally taken their place as sources of electric 
current. 

The advantages of voltaic cells as electric generators are : 
(a) they are inexpensive, (b) they are easily taken from 
place to place, (c) they may be ready for instant use. 

The most desirable voltaic cell would be one having the 



CURRENT ELECTRICITY 



275 




following qualities: (a) High electromotive force, (b) no 
polarization or local action, (c) very low internal resis- 
tance, d) small expense, both as to first cost and upkeep. 

249. The Leclanche cell is the one commonly used for 
ringing door bells. It has two plates : one of zinc and the 
other of carbon. These are placed in a solution of sal 
ammoniac (Fig. 222). Take up the desirable qualities 
mentioned at the end of the preceding paragraph, (a) 
It may be shown that this cell has a good E.M.F. about 
1.5 volts, (b) It polarizes easily yet it recovers well when 
left upon open circuit. Usually 
a substance called manganese 
dioxide is mixed with the carbon. 
This acts as a depolarizer that 
is, it combines with the hydro- 
gen to form water, (c) Its 
resistance varies and is often 

considerable, (d) The expense Fl <>- 222. The Leclanch6 cell, 
. . "wet" type. 

for upkeep is small, since a 

5-cent rod of zinc, and a 5-cent charge of sal ammo- 
niac will keep the cell in action on a bell circuit from six 
months to a year or more. It is well suited for use on 
open circuits that is, where the circuit is open the greater 
part of the time and is closed only occasionally; as in 
ringing door bells, operating telephones, and other devices 
whose circuits are usually open. 

250. The Dry Cell. Many forms of Leclanche cells 
are made. One of these is called the dry cell (See Fig. 
223.) In this cell the zinc plate is made into a jar or can 
and contains the other materials. At the center of the 
cell is a rod of carbon and manganese dioxide. The 
space between the carbon and zinc is filled with a porous 
material such as sawdust or plaster of Paris. A strong 
solution of sal ammoniac fills the porous material. The 



276 



PHYSICS 




Fig. 



The Leclanch6 
'dry" type. 



top of the cell is sealed with pitch or wax to prevent 
evaporation. The great advantage of this cell is that it 
may be used or carried in any position without danger 
of spilling its contents. Dry cells are often used to 
operate the spark coils of gas and 
gasoline engines. The Leclanche 
cell described in Art. 249 is com- 
monly known as the "wet cell." 

251. The Daniell Cell This 
cell is often used in laboratories, 
and on closed circuits such as those 
connected with fire and burglar 
alarms and telegraph lines. It 
has two plates of zinc and copper 
placed in two different liquids 
which are kept separated by a porous clay cup (Fig. 224). 
The zinc rod is kept in a solution of zinc sulphate con- 
tained in the porous cup. The copper plate is in a solution 
of copper sulphate filling the rest of the glass jar. Unlike 
the Leclanche cell, this one must be kept upon a closed 
circuit to do its best work, as 
the two liquids mix when the 
circuit is open. Taking its 
qualities in order, (a) its 
E.M.F. is about one volt, (b) 
it has no polarization since 
copper instead of hydrogen 
is deposited upon the copper 
plate. Therefore a uniform 
E.M.F. may be obtained 

from it, making it especially useful in laboratory experi- 
ments and tests, (c) Its resistance is considerable and (d) 
it is more expensive to operate than the Leclanche. It is 
sometimes used upon closed circuits outside of laboratories 




Fig. 224. The Daniell cell. 



CURRENT ELECTRICITY 



277 



as in burglar and fire alarms, although in recent years, the 
storage battery is taking its place for these purposes. 

252. The Gravity Cell. Fig. 225 is like the Daniell cell 
in most respects, except that in this cell, the zinc plate is 
held at the top of the jar in a solu- 
tion of zinc sulphate while the cop- 
per plate is at the bottom, sur- 
rounded by a solution of copper 
sulphate. The solutions mix but 
slowly as the copper sulphate 
solution is denser and remains at 
the bottom. This cell like the 
Daniell must also be kept upon 
closed circuit. On account of its 
simplicity and economy it is often 
used to operate telegraph instru- 
ments. Its qualities are similar Fig. 225. The gravity cell, 
to those of the Daniell cell. 

253. Symbol for Voltaic Cells. In electrical diagrams, 
the symbol employed to represent a voltaic cell is a short 
thick line near to and parallel to a longer thin one. As 
in Fig. 226 If several cells are to be represented the 
conventional symbol of the combination is represented as 




H 



Fig. 226. Diagram of 
a single cell. 



-I 



I I 



H= 



Fig. 227. Diagram of a group of 
cells. 



in Fig. 227. A single cell and a group of cells are each 
frequently called a battery. 

254. Effects of Electric Currents. Having studied 
some of the devices for producing an electric current, let 




278 PHYSICS 

us now consider some of the effects caused by it. These 
effects will be studied under three heads: (a) Magnetic, 
(b) Chemical, and (c) Heat effects. Devices or articles 
showing these effects known to most high school students 
are respectively: (a) the electromagnet (b) electro-plated 
silver ware and (c) electric heaters, such as electric flat 
r irons, electric toasters, etc. The mag- 

netic effect of an electric current was 
first detected by Oersted at the Uni- 
versity of Copenhagen in 1819. It may 
vanoscope. ga De observed by holding a wire carrying 
a current from a voltaic cell above and 
parallel to the needle of a magnetoscope. The needle 
is at once deflected (Fig. 228). If the current is reversed 
in direction the magnetoscope needle is deflected in the 
reverse direction. This simple device is the most com- 
mon means for detecting an electric current. It therefore 
constitutes a galvanoscope. (See Art. 239.) 

Important Topics 

1. Leclanche cells, (a), wet, (b), dry, construction, advantages, uses. 

2. Daniell and gravity cells, construction, advantages, uses. 

3. Three effects of electric currents, illustrations. 

4. The galvanoscope, uses. 

Exercises 

1. Explain how the direction of current in a wire can be determined 
by a compass. 

2. Would you expect to obtain a current from a zinc and copper cell 
containing a solution of common salt? Perform the experiment. 

3. What conditions in a voltaic cell will give a steady electromotive 
force. 

4. What conditions in a voltaic cell will give a strong electromotive 
force. 

5. Name three different electric circuits that you know exist. 
Which are open and which are dosed circuits? 

6. Are voltaic cells used in your home? If so, for what purpose are 
they used? On open or closed circuits? Have you seen them? 
What kind are they? 



CHAPTER XII 

THE MAGNETIC EFFECT OF ELECTRIC CUR- 
RENTS. ELECTRICAL MEASUREMENTS 

(i) The Magnetic Effect of Electric Currents 

255. The Magnetic Effect. Of all the effects of electric 
currents, it is generally conceded that the magnetic effect 
is the one of greatest practical importance, and it is also the 
one most extensively used. An experiment illustrating 
this effect has been described in Art. 239. This experi- 
ment shows that an electric current, if parallel to a mag- 
netic needle, and near it will deflect the north-seeking pole 
of the needle to the right or left depending upon the direc- 
tion of the current flow. This deflection of the magnetic 
needle is due to the fact that surrounding every electric 
current are magnetic lines of force. It is this magnetic 
field of the current that causes the needle to turn. The 
position taken by the needle is the resultant of the forces 
of two magnetic fields; one, the earth's field, the other, 
that of the current. 

256. Right-hand Rule for a Conductor. To show the 
presence of the magnetic field about a current, pass a thick 
copper wire vertically through a sheet of paper, and con- 
nect the ends of the wire to a source of current. While 
the current (this should be as much as 10 amperes if 
possible) is flowing, sprinkle iron filings upon the paper and 
tap gently. The filings will arrange themselves in circles 
about the wire showing the magnetic field. (See Fig. 229.) 
The needle of a magnetoscope tends to place itself parallel 
to the lines of force of this field and from this action or 

279 



280 



PHYSICS 



tendency the direction of the magnetic lines about a 
current may be determined. The following rule is helpful 
and should be memorized: Grasp the conductor with the 
right hand with the outstretched thumb in the direction that 
the current is flowing. The fingers will then encircle the 
wire in the direction of the lines of force. This rule may be 
reversed, for, if the fingers of the right hand grasp the 
wire so as to point with the magnetic field, then the 
current flows in the direction in which the thumb points. 
(See Fig. 230.) 

D/QECT/OH OF THE 
UHESOFFOffCE 





Fig. 229. Magnetic field Fig. 230. Right-hand rule for the mag- 
about a wire carrying an netic field of a current, 
electric current. 

257. Magnetic Field of a Helix. If a wire be wound 
about a cylinder to form a cylindrical coil with parallel 
turns, it forms a helix or solenoid. The shape of the 
magnetic field about a current depends upon the form 
of the conductor. If the latter is in the form of a helix its 
magnetic field resembles that of a straight bar magnet. 
(See Fig. 231). In fact the helix has the properties of a 
magnet with north- and south-seeking poles while a current 
is flowing through it. If such a coil is suspended so as to 
turn freely, it tends to turn until the field within it is 
parallel to the earth's magnetic field. Such a suspended 
helix may therefore be used as a compass. In order to 
strengthen' the magnetic field of a helix or solenoid, the 
space within its turns is filled with iron, often in the form 



MAGNETIC EFFECT OF ELECTRIC CURRENTS 28 1 

of small soft-iron wires. This bundle of iron wire is called 
the core of the helix. The core becomes strongly mag- 
netized by the field of the helix while the current is flowing 
and quickly loses its magnetic force when the current is 
stopped. The direction of the current in a helix (Fig. 232) 
or the polarity of its core may be determined by another 
right-hand rule. If the helix is grasped with the right hand 
so that the fingers point in the direction in which the current 
is flowing, the extended thumb will point in the direction of 
the north pole of the helix. On the other hand, if the 





Fig. 231. The magnetic field of a Fig. 232. Right-hand rule 
helix. for a helix. 

poles of the helix are known, then, when the -helix is 
grasped with the right hand so that the thumb points to 
the north-seeking pole, the current is flowing in the wires 
in the direction that the fingers point. 

258. The Electromagnet. These "right-hand" rules 
are applied in many different devices. Among these, 
perhaps the most important is the electromagnet, which 
is used in the electric bell, the telegraph, the tele- 
phone, the dynamo, the motor, and many other electric 
contrivances. 

The electromagnet is defined as a mass of iron around 
which is placed a helix for conducting an electric current. 
On account of its large permeability, the iron core of the 
helix adds greatly to the effectiveness of the electro- 
magnet, since the magnetism of the iron is added to that 
of the current in the helix. The magnetism remaining 



282 



PHYSICS 



in the iron after the current stops is called the residual 
magnetism. The residual magnetism is small when the 
core is made of small wires or thin plates, but is larger 
when the iron core is solid. Like artificial steel magnets, 





Fig. 233. A bar electromagnet. 



Fig. 



234. A horseshoe electro- 
magnet. 



electromagnets are usually of two forms, bar atid horseshoe. 
(See Figs. 233 #nd 234.) For most purposes the horse- 
shoe form is the more effective since it permits a complete 
iron circuit for the magnetic lines of force. (See Fig. 235.) 






' .in 
; 1 1 r. . 1 1 



^mimv t 




Fig. 235. A horseshoe elec- 
tromagnet may have a complete 
iron circuit for its lines of force. 



Fig. 236. A lifting 
magnet. 



This is the form used in the electric bell, in the telegraph 
sounder, and in lifting magnets. (See Fig. 236.) 

259. Effective Electromagnets. The magnetic effect 
of a current in a helix is small, hence the force usually is 
increased by inserting a core of iron. When at first man 



MAGNETIC EFFECT OF ELECTRIC CURRENTS 283 

tried to signal with electromagnets at a distance it was 
found that the current would not work the electromagnet. 
An American by the name of Joseph Henry discovered 
the remedy for this condition. He found that if the copper 
wire was insulated by wrapping silk thread about it, and 
then many layers of the silk insulated wire were wound upon 
a spool with an iron core, that the magnet would work at 
a great distance from the source of current. If the cur- 
rent is increased, the magnet is stronger than at first. 
Thus an electromagnet may be made stronger by (a) in 
creasing the number of turns of wire in its coils and by (b) 
sending a stronger current through it. 

260. The Telegraph. The invention of an effective 
electromagnet by Henry made possible the electric tele- 
graph. In its simplest form it consists of a battery, C, a 
key, K, and a sounder, 

S, with connecting wl^L v jjT'* " r ~J^ J -EJ 

wires. (See Fig. 237.) 5: S\ p" 

The sounder (Fig. 238) z: 
contains a horseshoe J- 
electromagnet and a bar FlG 237 _ A simpIe telegraph circ ^. 
of soft iron across its 

poles called an armature, A, attached to a lever L. When 
the key is closed, the electromagnet draws down the arma- 
ture and lever until the latter hits a stop O, making a 
click. When the key is raised, the magnet releases the 
armature which is raised by the action of a spring at S 
until the lever hits a stop at T making another click. 
Closing and opening the circuit at K will start and stop 
the current which operates S which may be 100 miles or 
more from K. One voltaic cell will work a sounder in 
the same room. But if many miles of wire are in the cir- 
cuit, the E.M.F. of a single cell will not force sufficient 
current through the long wire to operate the sounder. 



284 



PHYSICS 



A battery of several cells is then required. Even a 
large battery is insufficient to operate a long line containing 
many sounders in circuit. Recourse is therefore usually 

made to a more sen- 
sitive device called a 
relay. (See Fig. 239.) 
In the relay a very 
small current will mag- 
netize its electromag- 
net -enough to draw 
toward it the deli- 
cately hung armature 
thereby closing a sec- 
ond circuit which contains a sounder and a battery. (See 
Fig. 240.) When the current in the main circuit is 
stopped, the armature of the relay is drawn back by a light 
spring. This opens the local circuit. Thus the local cir- 




Fig. 238. A telegraph sounder. 



Sounder, 



.Key 




Tf K 1 

Local Battery % -g- 



line 



Fig. 239. A telegraph relay. 



Earth "->X-~ 

Fig. 240. How the relay 
is used. 



cuit is closed and opened by the relay just in time with 
the starting and stopping of the current in the main line. 
It is thus possible for a small current in the main line by 
the use of a relay, to close and open a second local circuit 



Samuel F. B. Morse (1791- 
1872). Inventor of the electro 
magnetic recording telegraph and 
of the dot and dash alphabet. 





Samuel F. B. Morse 
"From Appleton's Cyclopedia of 
American Biography, Copyright 
1888 by D. Appleton & Co." 



Thomas A. Edison, Orange, New 
Jersey. Invented the incandescent 
lamp; phonograph; moving picture; 
most noted inventor of electrical 
appliances of the present day. 



Thomas A. Edison 
"Copyright, Photographische 
Gessellschaft," and " By Permission 
of the Berlin Photographic Co., New 
York." 



MAGNETIC EFFECT OF ELECTRIC CURRENTS 



287 




Fig. 241. An electric bell and 
its circuit. 



containing a local battery and sounder. Modern telegraph 
lines are operated in this manner. 

261. The electric bell (see Fig. 241), consists of an 
electromagnet, M, a soft iron armature, A, attached to 
the tapper, T, and a post, R. When no current is flowing 
a spring at S holds the armature against the post R. 
When current flows through the helix, its core becomes 
magnetized and attracts the 
armature, drawing it away from 
the post, R, and causing the 
tapper to hit the bell. Draw- 
ing A away from the post, 
however, breaks the circuit at 
R and the current stops. The 
magnetism in the core disap- 
pears releasing the armature, which is then pulled back by 
the spring 5 against the post R. This completes the circuit 
and the process repeats itself several times a second as 
long as the current flows. 

262. Static and Current 
Electricity Compared/ The 
likeness between a discharge 
of static electricity and an 
electric current may be shown 
by winding a coil of insulated 
wire about a glass tube which 
contains a steel needle. If 

FlG dUc 4 ha7g"o a f S a n L^ n dLiar. the * ^^ J (see Kg. 24*) i 

discharged through the coil 

the steel needle is usually found to be magnetized, 

showing that the discharge of the static electricity has 

a magnetic effect similar to that of an electric current. 

Sometimes a given end of the needle has a north pole 

and at other times a south pole. This is believed to in- 




288 PHYSICS 

dicate that the charge of the Leyden jar is oscillatory, and 
that in different discharges sometimes a surge in one direc- 
tion and at other times a surge in the reverse direction 
has been most effective in magnetizing the needle. Com- 
pare this action with that described in Art. 233. 

Important Topics 

1. Right-hand rules, for conductor, for helix. 

2. The electromagnet, two forms, where used? 

3. Likeness between static and current electricity. 

4. The electric bell, parts, action. 

5. The telegraph, key, sounder, relay. 

Exercises 

1. What is the difference between an electric charge and a current ? 

2. How can a magnetic effect be produced from an electric charge? 

3. What is a magnetic field? Give two evidences .of a magnetic 
field about a current in a wire? 

4. A current is flowing north in trolley wire, what is the direction 
of the magnetic field under the wire? Explain. 

5. What would be the result if a hard steel core were placed in the 
electromagnet? Explain. 

6. If the north-seeking pole of a helix is facing you, does the cur- 
rent in the coils before you move in a clockwise or in a counter- 
clock wise direction? Explain. 

7. A helix is placed horizontally with its north-seeking pole toward 
the north. Does the current in the wire at the top of the helix 
move east or west? Explain. 

8. State at least six conditions any one of which will put an electric 
bell circuit out of commission. 

9. If one desires to insert a battery into a telegraph circuit already 
in operation, how will he determine the direction of the cur- 
rent in the wire. 

10. If a boy who had magnetized his knife blade in a physics labor- 
atory, pointed end south-seeking, should lose his way in the woods 
on a cloudy day, how could he determine his way out? 

11. At a certain point the earth's field acts north, that of an electric 
current, east. The magnetoscope needle points exactly north- 
east when placed at that point. How do the two magnetic 
fields compare? 



MAGNETIC EFFECT OF ELECTRIC CURRENTS 



289 



(2) Electrical Measurements 

263. Galvanometers. In using electric currents it is 
often necessary or desirable to be able to know not only 
that a given current is weak or strong, but precisely what 
its strength is. We can determine the relative strengths 
of two currents by the use of a galvanometer. 

The older or moving-magnet type of galvanometer is 
similar to the galvanoscope mentioned in Art. 239. It 





Fig 243. The magnet is at 
the center of the coil. 



Fig. 244. A moving-magnet 
(tangent) galvanometer. 



consists of a magnetic needle mounted at the center of a 
coil of wire. The coil is placed facing east and west, so 
that the needle will be held by the earth's magnetic field 
parallel to the plane of the coil. When a current is sent 
through the coil a magnetic field is produced within it. 
This deflects the needle, its north end turning east or 
west depending upon the direction of the current. (See 
Fig. 243.) The coils of a moving-magnet or tangent galva- 
nometer (see Fig. 244) are large and firmly fastened to the 
base, while the magnet is small. 

The moving-coil type of galvanometer (see Fig. 245) 
consists of a large magnet fastened to the frame of the 
device. The magnet usually has a horseshoe form to 

19 



290 



PHYSICS 



produce as strong a field as possible. The coil is wound 
on a light rectangular frame and is suspended between the 
two poles of the magnet. To concentrate the magnetic 
field, a cylinder of soft iron is usually placed within the 
coil. Fig. 246 represents a common form of moving-coil 
galvanometer. 



6 




Fig. 245. To illustrate 
the principle of the mov- 
ing-coil galvanometer. 



Fig. 246. A moving-coil 
(D'Arsonval) galvanometer. 



264. Measurement of Electric Currents. A galva- 
nometer enables one to compare electric currents. To 
measure electric currents it is necessary to employ a unit 
of electrical quantity, just as in measuring the quantity of 
water delivered by a pipe, a unit of liquid measure is 
employed; thus, e.g., the current delivered by a given pipe 
may be 2 gallons of water per second, so in measuring 
the flow of an electric current one may speak of two 
coulombs per second. The coulomb is the unit quantity 
of electricity just as the unit of quantity of water is the 
gallon. 

For most practical purposes, however, we are more 
interested in the rate or intensity of flow of current than in 



MAGNETIC EFFECT OF ELECTRIC CURRENTS 



291 



33= 



the actual quantity delivered. The unit of rate of flow 
or current is called the ampere. 

In determining the exact quantity of an electric current, 
physicists make use of a device called a coulomb meter. 
(See Fig. 247.) This contains a solution of silver nitrate 
in which are placed two silver plates. The current to 
be measured is sent through the solution, in at one plate 
and out at the other. The r 

plate where the current goes 
in,- the anode, A (Fig. 247), 
loses in weight since some of 
the silver is dissolved. The 
plate where the current goes 
out, the cathode, C, increases 
in weight since some of the 
silver is deposited. By an 
international agreement, the 
intensity of the current which 
deposits silver at the rate^ of 
0.001118 g. per second is 1 
ampere. This is equal to 
4.025 g. per hour. 

The coulomb is defined as 
the quantity of electricity 
delivered by a current of one ampere during one 
second. 

A 40-watt-incandescent lamp takes about 0.4 ampere of 
current. An arc lamp takes from 6 to 15 amperes. A 
new dry cell may send 20 amperes through a testing meter. 
A street car may take from 50 to 100 amperes. 

265. The Ammeter. The method described above is 
not used ordinarily for measuring current strengths on 
account of its inconvenience. The usual device employed 
is an ammeter. This instrument is a, moving-coil galva- 




Fig. 247. A coulomb meter, the 
anode A is separated from the 
cathode C by a porous cup. 



292 



PHYSICS 



nomeier. It contains, wound on a light form, a coil of fine 
copper wire. The form is mounted on jewel bearings 
between the poles of a strong permanent horseshoe magnet. 
(See Fig. 248.) As in other moving-coil galvanometers, a 
soft iron cylinder within the form concentrates the field 
of the magnet. The form and its coil is held in balance 
by two spiral springs which also conduct current into and 
out of the coil. 

Only a small part 
of the whole current 
measured, in some 
cases only 0.000 1 
passes through the 
coil, the larger part 
of the current pass- 
ing through a metal 
wire or strip called a 
shunt 1 (see Fig. 248) 
connecting the bind- 
ing posts of the in- 
strument. A fixed 
fraction of the whole 
current flows through 
the coil. Its field crossing the field of the horseshoe 
magnet, tends to turn until its turning force is balanced 
by the spiral springs. As the coil turns it moves a 
pointer attached to it across a scale graduated to indicate 
the number of amperes in the whole current. 

It should be noted that while all of the current measured 
passed through the ammeter, but a small part goes through 
the coil. 




Fig. 248. Diagram of a commercial am- 
meter. S is the shunt. 



X A shunt is a conductor or coil connected in parallel with another 
conductor or circuit. It carries- a part of the current. 



MAGNETIC EFFECT OF ELECTRIC CURRENTS 293 

266. Resistance of Conductors. With an ammeter 
one may study the change produced in the amount of 
current flowing in a wire when a change is made in the 
wire conducting the current. For example, if one meas- 
ures with an ammeter the current flowing from a dry 
cell through a long and then through a short piece of fine 
copper wire, it will be seen that less current flows when the 
long piece is used. That is, the long wire seems to hinder 
or to resist the passing of the current more than the short 
piece. In other words, the long wire is said to have more 
resistance. 

The resistance of a conducting body is affected by 
several conditions. 

(a) It is directly proportional to the length of the con- 
ductor, one hundred feet of wire having twice the resis- 
tance of fifty feet. 

(b) It is inversely proportional to the square of the 
diameter; a wire o.i inch in diameter has four times the 
resistance of a wire 0.2 inch in diameter. 

(c) It differs with different substances, iron having 
about six times as much as copper. 

(d) It varies with the temperature, metals having 
greater resistance at a higher temperature. 

Since silver is the best conductor known, the re- 
sistances of other substances are compared with it as a 
standard. 

The ratio of the resistance of a wire of any substance 
as compared to the resistance of a silver wire of exactly 
the same diameter .and length is called its relative 
resistance. 

Purified substances arranged in order of increasing 
resistance for the same length and sectional area (Ayrton- 
Mather) are given on p. 294. 



294 PHYSICS 

Silver annealed i.oo 

../from 1.04 

Copper annealed < 

Uo 1.09 

Aluminum annealed 1.64 

Nickel annealed 4.69 

Platinum annealed 6.09 

Iron annealed 6.56 

.. /from 12.80 

German silver < 

v. to 20.20 

Mercury 63.30 

Nichrome 67.50 

, ( from 2700.00 

Carbon < 

I to 6700.00 

267. The ohm, the unit of resistance, is defined by in- 
ternational agreement as follows: An ohm is the resistance 
of a column of pure mercury, 106.3 cm. long with a cross- 
section of a square millimeter and at a temperature of o C. 

It should be noted that each of the four conditions 
affecting resistance is mentioned in the definition, viz., 
length, cross-section, material, and temperature. Since it 
is inconvenient to handle mercury, standard resistance 
coils, made of an alloy of high resistance are used in com- 
paring and measuring resistances. 

A piece of copper wire No. 22 (diameter 0.644 mm.) 
60.5 ft. long has a resistance of 1 ohm. See table 
p. 296. 

The resistance of some telephone receivers is 75 ohms, 
of a telegraph sounder, 4 ohms, of a relay 200 ohms. 

268. Resistance of Circuits. Every part of an elec- 
trical circuit possesses resistance. In an electric-bell cir- 
cuit, for instance, the wires, the bell, the push-button, and 
the cell itself, each offers a definite resistance to the passage 
of the current. The resistance within the cell is termed 
internal resistance, while the resistance of the parts out- 
side of the electric generator is called external resistance. 



MAGNETIC EFFECT OF ELECTRIC CURRENTS 



295 



269. Electromotive Force. In order to set in motion 
anything, some force must be applied. This is as true of 
electricity as of solids, liquids, or gases. By analogy 
that which is exerted by a battery or by a dynamo in 
causing current to flow is called an electromotive force. 
The unit of electromotive force, the volt, may be de- 
fined as the electromotive force that will drive a current 
of 1 ampere through the resistance of 1 ohm. The electro- 
motive force of a dry 
cell is about 1.5 
volts, of a Daniell 
cell 1.08 volts. Most 
electric light circuits 
in buildings carry 
current at no or 
220 volts pressure. 
Currents for street 
cars have an elec- 
tromotive force of 
from 550 to 660 
volts. 

270. The Volt- 
meter. An instru. 
ment for measuring 

the electromotive force of electric currents is called a 
voltmeter (Fig. 249). It is usually a moving-coil galvan- 
ometer, and is always of high resistance. It is like an 
ammeter in construction and appearance. In fact, a volt- 
meter is an ammeter which has had its shunt removed or 
disconnected. In place of a shunt, the voltmeter uses a 
coil of wire of high resistance (see R, Fig. 249) in series with 
the galvanometer coil. The high resistance of the volt- 
meter permits but a very small current to flow through it. 
Hence a voltmeter must be placed across a circuit and 




Fig. 249.- 



-Diagram of a commercial volt- 
meter. 



296 



PHYSICS 



not in it. In other words a voltmeter is connected in 
shunt, while an ammeter is in series with the circuit as is 
shown in Fig. 250. 

Dimensions and Functions of Copper Wires 



B. AS. 


Diameter 


Circular 
mils 


Sectional 
area in 
square 
milli- 
meters 


Weight 

and length. 

Density = 8.9, 

feet per 

pound 


Resistance 

at 24C, 

feet per 

ohm 


Capacity 


gauge 
number 


Mils 


Milli- 
meters 


in 
amperes 


0000 
000 


460 . 000 
409 . 640 


11.684 
10. 405 


211,600.00 
167,805.00 


107.219 
85.028 


1.56 
1.97 


19,929.700 
IS. 804. 900 


312.0 
262.0 


00 


364.800 


9.266 


133,079 40 


67.431 


2.49 


12,534.200 


220.0 



2 


324.950 
257.630 


8.254 
6.544 


105.592.50 
66,373 00 


53470 
33631 


3.13 
4-99 


9.945-300 
6,251 .400 


185.0 
131-0 


4 

6 

8 

10 


204.310 
162.020 
128.490 
101.890 


5. 189 
4-H5 
3.264 
2 588 


41,742.00 
26,250.50 
16,509 00 
10,381.00 


21. 151 

13301 

8.366 

5.260 


793 
12.61 
20.05 
3138 


3,931 .600 

2,472.400 

1,555-000 

977.800 


92.3 
65.2 
46.1 
32.5 - 


12 
14 


80.808 
64.084 


2.053 
1.628 


6,52990 
4,106.80 


3309 
2.081 


50.69 
80.59 


615 020 
386.800 


23.0 
16.2 - 


16 


50.820 


1. 291 


2,582.90 


1.309 


128.14 


243 250 


11. 5 


18 
20 


40.303 
31.961 


1.024 
0.812 


1,624.30 
1,021 .50 


0.823 
0.5176 


203 76 
324.00 


152.990 
96.210 


8.1 
5-7 


22 


25.347 


0.644 


642.70 


0.3255 


515-15 


60.510 


4-0 


24 


20.100 


0.511 


504.01 


0.2047 


819.21 


38.OSO 


2.8 


26 


15-940 


0.40s 


254.01 


0.1288 


1,302.61 


23930 


2.0 


28 


12.641 


0.321 


159-79 


0.08097 


2,071 .22 


15. 050 


1-4 ' 


30 
32 


10. 02s 
7-950 


0.255 
O.202 


100.50 
63.20 


0.05092 
0.03203 


3.293-97 
5,236.66 


9466 
5-952 


I .0 

0.70 


34 
36 


6.304 
5-000 


O.160 
O.127 


3974 
25.OO 


0.02014 
0.01267 


8,328.30 
13.238.83 


3-743 
2.35S 


0.50 

0.35 


38 


3965 


0. 101 


1572 


0.00797 


20.854.65 


1. 481 


0.2s 


40 


3.144 


0.080 


989 


0.00501 


33.17594 


0.931 


0.17 



Important Topics 

(1) Galvanometers: (i) moving magnet, fixed coil; (2) moving coil, 
fixed magnet, ammeter, voltmeter. 

(2) Unit of quantity, coulomb. 

(3) Unit of current, ampere. 

(4) Unit of resistance, ohm. 

(5) Unit of electromotive force, volt. 



MAGNETIC EFFECT OF ELECTRIC CURRENTS 



297 



Exercises 

1.. How will the resistance of 20 ft. of No. 22 German silver wire 
compare with that of 10 ft. of No. 22 copper wire? Explain. 

2. Where in a circuit is copper wire desirable? Where should 
German silver wire be used? 

3. Explain the action of the ammeter. Why does not the needle 
or coil swing the full distance wth,a small current? 

4. Why is a telegraph sounder more apt to work on a short line 
than upon a long one? 




V^ 



Fig. 250. The ammeter is connected in series and the voltmeter in shunt. 

5. Find the resistance of 15 miles of copper telephone wire No. 12. 
(See table p. 296.) 

6. What will be the weight and resistance of 1,000 feet of No. 20 
copper wire? 

7. A storage battery sends 4 amperes of current through a plating 
solution. How much silver will it deposit in 2 hours? 

8. (a) Compare the diameters of No. 22 and No. 16 copper wire. 

(b) Compare the lengths of the same wires giving 1 ohm resis- 
tance. 

(c) What relation exists between (a) and (b) ? 

9. Why is an electric bell circuit usually open while a telegraph 
line circuit is usually closed? 

10. A copper wire and an iron wire of the same length are found to 
have the same resistance. Which is thicker? Why? 

11. Why are electric bells usually arranged in parallel instead of in 
series? 

12. What would happen if a voltmeter were put in series in a line? 



298 PHYSICS 

(3) Ohm's Law and Electrical Circuits 

271. Conditions Affecting Current Flow. Sometimes 
over a long circuit one cell will not work a telegraph 
sounder. In such a case, two, three, or more cells are 
connected so that the zinc of one is joined to the 
copper plate of the other. When connected in this way 
the cells are said to be in series (Fig. 251). In the 
figure A represents a voltmeter. It is found that when 
cells are in series the E.M.F. oj the battery is the sum 

0] the electromotive forces oj the cells. 

I a I * I 1 |_ An ammeter in the circuit shows in- 

l 1 1 I 1 creased current as the cells are added. 
Hence ij the resistance of the circuit 
remains unchanged, the greater the 
Fig. 251. Diagram E.M.F. the greater is the current 
serie C s dlS connected m strength. In this respect, the move- 
ment of electricity in a circuit is simi- 
lar to the flow of water in a small pipe under pressure, 
as in the latter the flow of water increases as the pressure 
becomes greater. The current in a circuit may also be 
increased by lessening the resistance, since the current 
through a long wire is less than that through a short one, 
just as the flow of water will be greater through a short 
pipe than through a long one. To increase the current 
flowing in an electric circuit, one may therefore either 
increase the E.M.F. or decrease the resistance. 

272. Ohm's Law. The relation between the electro- 
motive force applied to a circuit, its resistance, and the 
current produced was discovered in 1827 by George Ohm. 
Ohm's law, one of the most important laws of electricity, 
states that, in any circuit, the current in amperes equals 
the electromotive force in volts divided by the resistance in 
ohms. 



MAGNETIC EFFECT OF ELECTRIC CURRENTS 299 

This principle is usually expressed thus: 

" - . . electromotive force 

Current intensity = r or 

' resistance 

volts _ E 
Amperes = -j- or /= ^ 

273. Resistance of Conductors in Series. A study of 
the resistance of conductors when alone and when grouped 
in various ways is of importance since, the current flow 
through any circuit is dependent upon its resistance. The 
two most common methods of combining several conduc- 
tors in a circuit are in series and in parallel. Conductors 
are in series when all of the current passes through each of 
the conductors in turn 



(Fig. 218), thus the cell, f gjg Q j|Sm|j O 

push-button, wires, and " w ' ' u - 1 - 

electric bell in an eleC- Fl G- 252. The street cars are connected 
. . ., . in parallel with each other. 

tnc-bell circuit are m 

series. Conductors are in parallel when they are so 
connected that they are side by side and a part of 
the whole current goes through each. None of the cur- 
rent that passes through one conductor can go through 
the conductors in parallel with it. Thus the electric 
street cars are in parallel with each other. (See Fig. 252.) 
It is easily seen that none of the current passing through 
one car can go through any of the others. When the con- 
ductors are in series the combined resistance is the sum 
of the several resistances. Thus in an electric-bell cir- 
cuit if the battery has a resistance of 1 ohm, the bell of 
2 ohms, and the wire 1 ohm, the total resistance in the 
circuit is 4 ohms. When conductors are in parallel the 
combined resistance is always less than the separate re- 
sistances. Just as a crowd of people meets less resistance 
in leaving a building through several exits, so electricity 




300 PHYSICS 

finds less resistance in moving from one point to another 
along several parallel lines, than along one of the lines. 
274. Resistance of Conductors in Parallel. If three 
conductors of equal resistance are in parallel, the com- 
bined resistance is just one-third the resistance of each 
separately (Fig. 253). The rule that states the relation 
between the combined resistance of conductors in parallel 
and the separate resistances is as follows: The combined 

resistance of conductors in par- 
allel is the reciprocal of the sum 
of the reciprocals of the several 
resistances. For example, find 
the combined resistance of 
three unequal resistances in 
Fig. 253. The three conductors parallel; the first being 4 ohms, 

are connected in parallel. , , , , , , , , . , 

the second, 6 ohms, and third 
3 ohms. The reciprocals of the three resistances are \ y , 
}, and ><$. Their sum equals % A + ^4 + % A = *% A . 
The reciprocal of this is 2 j>{s which equals 1^ ohms, the 
combined resistance. 

This rule may be understood better if we consider the conductance 
of the conductors in parallel. Since the conductance of a two ohm 
wire is just one-half that of a one-ohm wire, we say that the conduc- 
tance of a body is inversely as the resistance, or that it is the recipro- 
cal of the resistance. The conductance of the 4-, 6-, and 3-ohm coils 
will therefore be respectively K, 2^, and %, and since the com- 
bined conductance is the sum of the several conductances, the total 
conductance is x %4,. Also since this is the reciprocal of the total 
resistance, the latter is 2 ^ 8 or iK ohms. 

When two or more conductors are connected in parallel 
each one is said to be a shunt of the others. Many circuits 
are connected in shunt or in parallel. Fig. 254 represents 
four lamps in parallel. Incandescent lamps in buildings 
are usually connected in parallel, while arc lamps are 



MAGNETIC EFFECT OF ELECTRIC CURRENTS 3OI 

usually connected in series. Fig. 255 represents four 
lamps in series. 

Important Topics 

1. Conditions affecting current flow, (a) E.M.F., (b) resistance. 

2. Ohm's law, three forms for formula. 

3. Resistance of conductors: (a) in series, (b) in parallel; how com- 
puted, illustrations. 

Fig. 254. The four lamps are Fig. 255. The four lamps are 
connected in parallel. connected in series. 

Exercises 

1. What current flows through a circuit if its E.M.F. is no volts 
and the resistance is 220 ohms? 

2. A circuit contains four conductors in series with resistances of 
10, 15, 6, and 9 ohms respectively. What current will flow 
through this circuit at no volts pressure? What will be the 
resistance of these four conductors in parallel ? 

3. What is the combined resistance of 8 conductors in parallel 
if each is 220 ohms? What current will flow through these 
8 conductors at no volts pressure? 

4. What is the resistance of a circuit carrying 22 amperes, if the 
E.M.F. is 20 volts? 

5. What E.M.F. will send 8 amperes of current through a circuit 
of 75 ohms resistance? 

6. How does the voltmeter differ from the ammeter? 

7. How can one determine the resistance of a conductor? 

8. The resistance of a hot incandescent lamp is 100 ohms. The 
current used is 1.1 amperes. Find the E.M.F. applied. 

9. What is the resistance of the wires in an electric heater if the 
current used is 10 amperes, the voltage being no? 

10. The resistance of 1000 ft. of No. 36 copper wire is 424 ohms. 
How many feet should be used in winding a 200 ohms relay? 

11. The resistance of No. 00 trolley wire is 0.80 ohm per 1000 ft. 
What is the resistance of a line 1 mile long? 

12. A wire has a resistance of 20 ohms. It is joined in parallel with 
another wire of 6 ohms, find their combined resistance. 



3 2 



PHYSICS 



13. The separate resistances of two incandescent lamps are 200 ohms 
and 70 ohms. What is their combined resistance when joined 
in parallel? When joined in series? 



(4) Methods of Grouping Cells and Measuring 
Resistance 

275. Internal Resistance of a Voltaic Cell. The current 
produced by a voltaic cell is affected by the resistance 
that the current meets in passing from 
one plate to another through the liquid 
of the cell. This is called the internal 
resistance of the cell. A Daniell cell 
has several (1-5) ohms internal resis- 
tance. The resistance of dry cells varies 
from less than 0.1 of an ohm when new 
to several ohms when old. If cells are 
joined together their combined internal 
resistance depends upon the method of 
grouping the cells. 

276. Cells Grouped in Series and 
in Parallel. When in series the copper 
or carbon plate of one cell is joined to 
the zinc of another and so on. (See 
Fig. 251.) The effect of connecting, 
say four cells, in series may be illus- 
trated by taking four cans of water, 
placed one above another. (See Fig. 
256.) The combined water pressure of 
the series is the sum of the several 
pressures of the cans of water, while 
will the opposition offered to the movement 
of a quantity of water through the group 
of cans is the sum of the several resistances of the cans. 
In applying this illustration to the voltaic cell, we make 



Fig. 256. The four 
cans exert four times 
the water pressure 
that one can 
exert. 



MAGNETIC EFFECT OF ELECTRIC CURRENTS 



303 



use of Ohm's law. Let E represent the e.m.f. of a single 
cell, r the internal resistance of the cell, and R the external 
resistance or the resistance of the rest of the circuit. 
Consider a group of cells in series. If n represents the 
number of cells in series, then Ohm's law becomes 



/ = 



nE 



nr + R 



Cells are grouped in series when large E.M.F. is required 
to force a current through a large external resistance such 
as through a long telegraph line. Cells 
are connected in parallel when it is desired 
to send a large current through a small 
external resistance. To connect cells in 
parallel all the copper plates are joined 



UtXi 



Fig. 257. Four 
cells connected in 
parallel. 



Fig. 258. The water pressure of 
the group in parallel is the same as 
that of one. 



and also all the zinc plates. (See Fig. 257.) To illustrate 
the effect of this mode of grouping cells, suppose several 
cans of water are placed side by side (Fig. 258). It is 
easily seen that the pressure of the group is the same as 
that of a single cell, while the resistance to the flow is less 
than that of a single cell. Applying this reasoning to 
the electric circuit we have by Ohm's law the formula for 
the current flow of a group of 

E 

n cells arranged in parallel / = 

- + R 



304 ' PHYSICS 

277. Illustrative Problems. Suppose that four cells 

are grouped in parallel, each with an E.M.F. of 1.5 volts 

and an internal resistance of 2 ohms. What current will 

flow in the circuit if the external resistance is 2.5 ohms? 

Substitute in the formula for cells in parallel the values 

1.5 1.5 

given above, and we have / = r = = 0.5 

0.5 + 2.5 3 

ampere. Suppose again that these four cells were grouped 

in series with the same external resistance, substituting 

the values in the formula for cells in series we have / = 

4(1.5) 6 

; = = 0.57 ampere. 

4X2 + 2.5 10.5 9i F 

278. Volt-ammeter Method for Finding Resistance. 

Measurements of the resistance of conductors are often 
made. One of these methods depends upon an applica- 
tion of Ohm's law. It is called the volt-ammeter method 
since it employs both a voltmeter and an ammeter. If 
the conductor whose resistance is to be measured is made 
a part of an electric circuit, being connected in series with 
the ammeter and in shunt with the voltmeter, the resistance 

may easily be determined, since R = (See Fig. 250.) 

If, for example, the difference in E.M.F., or as it is often 
called, the fall of potential between the ends of the wire 
as read on the voltmeter is 2 volts, and the current is 
0.5 ampere, then the resistance of the wire is 4 ohms. 
This method may be readily applied to find the resistance 
of any wire that is a part of an electric circuit. 

279. The Wheatstone Bridge. To find the resistance 
of a separate wire or of anelectrical device another method 
devised by an Englishman named Wheatstone is commonly 
employed. This method requires that three known 
resistances, a, b, c, in addition to the unknown resistance 



MAGNETIC EFFECT OF ELECTRIC CURRENTS 



305 



x be taken. These four resistances are arranged in the 
form of a parallelogram. (See Fig. 259.) A voltaic cell is 
joined to the parallelogram at the extremities of one diag- 
onal while a moving-coil galvanometer is connected across 
the extremities of the- other diagonal. The known re- 
sistances are changed until when on pressing the keys 
at E and K no current flows through the galvanometer. 
When this condition is 
reached, the four resistances 
form a true proportion, thus 
a : b = c : x. 

Since the values of a, b, 
and c are known, x is readily 
computed. Thus if a = 10, 
b = 100, and c = 1.8 ohms, 
then x, the unknown resis- 
tance, equals 18 ohms, since 
10 : 100 = 1.8 : 18. This 
method devised by Wheat- 
stone may be employed to find the resistance of a great 
variety of objects. It is the one most commonly employed 
by scientists and practical electricians. 




Fig. 259. 



-Diagram of a Wheat- 
stone bridge. 



Important Topics 

1. The internal resistance of voltaic cells. 

2. Ohm's law applied to groups of cells, (a) Cells in series, (b) 
cells in parallel. 

3. Measurement of resistance: (a) volt-ammeter method, (b) 
Wheatstone bridge method. 



Exercises 

1. What is the resistance of an electric bell circuit where the E.M.F. 
is 3 volts and the current is 0.6 ampere? 

2. A telegraph wire is broken somewhere, the ends lying upon damp 
ground. If an E.M.F. of 30 volts is applied from the ground 

20 



306 PHYSICS 

to the wire and a current of o.i of an ampere flows, what is the 
resistance of the part connected to the ammeter. (The earth 
which completes the circuit from the end of the wire has very 
small resistance.) Why? 

3. How far away is the break in the wire if the latter has a resis- 
tance of 80 ohms to the mile? Diagram. 

4. What current will flow through a bell circuit of 8 ohms resistance 
if it contains three cells in series each with an E.M.F. of 1.5 
volts and an internal resistance of ^ ohm? 

5. If the same three cells are connected in parallel on the same cir- 
cuit what current flows? Is the current in problem 4 or 5 the 
larger? Why? 

6. If four cells each with 1.5 volts E.M.F. and an internal resistance 
of 0.4 ohm are connected with a circuit having an external 
resistance of 0.8 ohm, what current will the parallel connection 
give? The series connection? Which gives the larger current? 
Why? 

7. Four Daniell cells each having 1 volt E.M.F. and 3 ohms internal 
resistance are connected in series with 2 telegraph sounders of 
4 ohms each. The connecting wires have 6 ohms resistance. 
Find the current intensity. 

8. A battery of 2 cells arranged in series is used to ring a door bell. 
The E.M.F. of each cell is 1.5 volts, internal resistance 0.3 ohm, 
and the resistance of the bell is 4 ohms. What is the current 
in amperes? 

9. In the above problem find the current if the cells are connected 
in parallel. 



CHAPTER XIII 



THE CHEMICAL AND HEAT EFFECTS OF 
ELECTRIC CURRENTS 

(i) The Chemical Effect of an Electric Current 

280. Electroplating. If two carbon rods (electric light 
carbons answer very well) are placed in a solution of 
copper sulphate (Fig. 260) and then connected by wires to 
the binding posts of an electric battery, one of the rods 
soon becomes covered with a coating of metallic copper 
while bubbles of gas may be seen upon 
the other carbon. If a solution of lead 
acetate is used in the same way a deposit 
of metallic lead is secured, while a 
solution of silver nitrate gives silver. 



3r* 





Fig. 260. Two car- 
bons placed in a solu- 
tion of copper sulphate. 



Fig. 261. An electroplating bath. 



This process of depositing metals upon the surface of 
solids by an electric current is called electroplating. 
Everyone has seen electroplated articles such as silver 
plated knives, forks, and spoons, and nickel-plated rods, 
handles, etc. Copper electrotype plates such as are used 
in printing school books are made by this process. In 

307 



3 o8 



PHYSICS 



practical electroplating a solution of the metal to be de- 
posited is placed in a tank; across the top of this tank are 
placed copper rods to act as conducting supports. From 
one of these rods, the cathode, objects to be plated are 
hung so as to be immersed in the liquid. From other rods, 
the anodes, are hung plates of the metal to be deposited. 
These are dissolved as the current deposits a coating upon 

the articles, thus keeping the 
solution up to its proper 
strength. (See Fig. 261.) 

281. Electrolysis. A solu- 
tion from which a deposit is 
made by an electric current is 
called an electro.lyte. The 
plates or other objects by 
which the current enters or 
leaves the electrolyte are called 
the electrodes. The electrode 
by which the current enters 
is called the anode (an = in) 
while the electrode by which 
it leaves is the cathode (cath = 
away) . The process by which 
an electric current decomposes 
a solution and deposits a sub- 
stance upon an electrode is called electrolysis. The current 
always flows within the cell from anode to the cathode. 
(See Fig. 262.) The metal goes with the current and is 
found deposited upon the cathode. 

282. Theory of Electrolysis. The action going on in 
an electrolytic cell has been carefully studied. The theory 
of electrolysis, which is supported by much experimental 
evidence, supposes that many of the molecules in a dilute 
solution of a substance "split up" into two parts called 






Fig. 262. The current is car- 
ried through the solution by ions 



CHEMICAL AND HEAT EFFECTS 



39 



f 



H' ' 



f 



-*0 



"ions," one ion having a positive, the other a negative 
charge. In a dilute solution of sulphuric acid, the positive 
ion is of hydrogen, while the negative ion is the (SO4) or 
sulphion. These ions bearing electric charges are believed 
to be the carriers of the electric current through the 
electrolyte. 

The positive ions move with the current from the anode 
to the cathode, while the negative ions apparently are 
repelled by the cathode and appear upon the anode. 
Evidence of the accumulation of T 

the two kinds of ions at the two 
electrodes is furnished by the elec- 
trolysis of water, described below. 

283. Electrolysis of Water. Two 
glass tubes (Fig. 263), H and 0, are 
attached at the bottom to a hori- 
zontal glass tube. To the latter is 
also connected an upright tube T. 
At the lower ends of H and O are 
inserted, fused in the glass, platinum 
wires, A and C. The tubes are filled 
with a weak solution of sulphuric 
acid. The tops of H and O are 
closed with stopcocks, T being 
open; a current of electricity is 
sent in at A and out at C. A 
movement of the ions at once be- 
gins, the positive hydrogen ions appearing at C. These 
accumulate as bubbles of hydrogen which rise to the 
top of H and displace the liquid. At the same time 
bubbles of oxygen appear at A . These rise in and also 
displace the liquid which rises in T. After the action has 
continued some time it may be noticed that the volume 
of hydrogen is just twice that of the oxygen. This was 




Fig. 2 63 . Electrolysis 
of water; oxygen collects 
in 0, hydrogen in H. 



3io 



PHYSICS 



to have been expected since the formula for water is H 2 0. 
The nature of the gas in H or O may be tested by opening 
the stopcock and allowing the gas to escape slowly. The 
hydrogen gas can be lighted by a flame while the oxygen 
gas will cause a spark upon a piece of wood to glow brightly, 
but does not burn itself. 

284. Evidence that ions are necessary to conduct a 
current in a liquid is furnished by the following experi- 
ment. A quart jar is carefully cleaned, and half filled with 
distilled water. Two pieces of zinc 5 cm. square are 
soldered to pieces of rubber-insulated No. 14 copper wire. 

The zincs are placed in the 
distilled water (Fig. 264) and 
the wires are connected to a 
no volt circuit with a 16 
candle-power incandescent 
lamp in series with the cell, as 
in the figure. If the zincs have 
been carefully cleansed and the 
water is pure, no current flows 
as is shown by the lamp re- 
maining dark. If a minute quantity of sulphuric acid 
or of common salt is placed in the water the lamp at 
once begins to glow. Ions are now present in the liquid 
and conduct the current. That some substances in solu- 
tion do not form ions may be shown by adding to another 
jar of pure water some glycerine and some cane sugar, sub- 
stances resembling the acid and salt in external appear- 
ance but which do not ionize when dissolved as is shown 
by the lamp remaining dark after adding the glycerine 
and sugar. The acid and salt are of mineral origin while 
the glycerine and sugar are vegetable products. This 
experiment illustrates the principle that the water will 
conduct only when it contains ions. 




Fig. 264. The current passes 
only when ions are present in the 
liquid. 



CHEMICAL AND HEAT EFFECTS 311 

285. Laws of Electrolysis. These were discovered by 
"Faraday in 1833, and may be stated as follows: /. The 
mass oj a substance deposited by an electric current from 
an electrolyte is proportional to the intensity of current 
which passes through it." 

II. The mass oj any substance deposited by a current of 
uniform intensity is directly proportional to the time the 
current flows. 

These laws have been used as a basis for defining and 
measuring the unit of current flow, the ampere. (See 
Art. 264.) 

286. Instances of Electrolysis. (a) Medicines, espe- 
cially those containing a mineral substance, are sometimes 
introduced into the human body by electrolysis, (b) 
Water and gas pipes are sometimes much weakened by 
the effects of electric currents in the earth, especially 
return currents from street railways. Such currents use 
the metal pipes as a conductor. At the place where the 
current leaves the metal and enters the ground, it removes 
metallic ions from the pipe. This process continuing, 
the pipe becomes weakened and at length breaks, (c) 
Copper is purified by the use of electric currents that 
remove the copper from ore or from other metals and de- 
posit it upon electrodes. Electrolytic copper is the purest 
known, (d) Aluminum is obtained by the use of large 
currents of electricity that first heat the material used until 
it melts and then deposit the metal from the fluid material 
by electrolysis. These results are called chemical effects 
of the current since by the use of electric currents sub- 
stances are changed chemically, that is, they are separated 
into different chemical substances. 



312 PHYSrCS 

Important Topics 

i. Electrolysis, electroplating, anode, cathode, ion. 

2. Theory of electrolysis evidence: (a) electrolysis of water; (b) 
conductivity of acid and water. 

3. Laws of electrolysis. 

4. Practical use of electrolysis. 

Exercises 

1. A dynamo has an E.M.F. of 10 volts. What is the resistance in 
the circuit when 20 amperes are flowing? 

2. How much silver will be deposited in an hour by this current? 

3. Name five objects outside of the laboratory that have been acted 
upon by electrolysis. How in each case? 

4. Why is table ware silver plated? Why are many iron objects 
nickel plated? 

5. How is the electrolysis of water pipes prevented? 

6. Two grams of silver are to be deposited on a spoon by a cur- 

rent of 1 ampere. Find the time required. 

7. How long will it take to deposit 20 g. of silver in an electro- 
plating bath if a current of 20 amperes is used? 

8. If 1000 g. of silver are deposited on the cathode of an electro- 

lytic reduction plant in 10 minutes, what is the current inten- 
sity employed? 

(2) The Storage Battery and Electric Power 

287. Differences Between Voltaic and Storage Cells. 

Volaic cells in which electric currents are produced by 
the chemical action between metal plates and an elec- 
trolyte are often called primary batteries. In voltaic 
cells one or both plates and the electrolyte are used up 
or lose their chemical energy in producing the current 
and after a time need to be replaced by new material, the 
chemical energy of the electrolyte and of one of the plates 
having been transformed into electrical energy. 

A different proceeding obtains with another type of 



CHEMICAL AND HEAT EFFECTS 313 

cell. This is called a storage battery, or an accumulator. 
In these cells, the same plates and electrolyte are used 
without change for extended periods, sometimes for a 
number of years. For this reason storage batteries have 
displaced many other types of cells, and they are now 
used (a) to operate many telephone, telegraph, and fire- 
alarm circuits, (b) to work the spark coils of gas and 
gasoline engines, (c) to help carry the "peak" load upon 
lighting and power circuits and (d) to furnish power for 
electric automobiles. Since a storage battery can deliver 
an electric current only after an electric current from an 
outside source has first been sent through it, they are 
often called secondary batteries. 

288. Construction and Action of a Storage Cell. The 
common type of storage cells consists of a number of 
perforated plates made of an alloy of lead and a little 
antimony. (See Figs. 265, 266, 267.) Into the perfora- 
tions is pressed a paste of red lead and litharge mixed 
with sulphuric acid. The plates are placed in a strong 
solution (20 to 25 per cent.) of sulphuric acid. The plates 
are now ready to be charged. This is accomplished by 
sending a direct current from an electric generator through 
the cell. The hydrogen ions are moved by the current 
to one set of plates and change the paste to spongy me- 
tallic lead. The sulphions move to the other set of plates 
and change the paste to lead oxide. This electrolytic 
action 'causes the two plates to become quite different 
chemically so that when the cell is fully charged it is 
like a voltaic cell, in having plates that are different 
chemically. It has, when fully charged, an E.M.F. of 
about 2.2 volts. The several plates of a cell being in 
parallel and close together, the cell has but small internal 
resistance. Consequently a large current is available. 

About 75 per cent, of the energy put into the storage cell 



314 



PHYSICS 



in charging can be obtained upon discharging. Therefore 
the efficiency of a good storage cell is about 75 per cent. 
Fig. 268 represents a storage battery connected to charg- 





mna 



::s 



265. The positive plate 
of a storage cell. 



Fig. 



266. The negative plate 
of a storage cell. 



ing and discharging circuits. The lower is the charging 
circuit. It contains a dynamo and a resistance (neither 
of which are shown in the figure) to control. the current 

sent into the cell. The charging 
current enters the positive pole 
and leaves by the negative pole. 
The current produced by the 
cell, however, flows in the oppo- 
site direction through it, that is, 
out from the positive and in at 

R N 




p^VV\A/W^-j 




Fig. 267. A complete storage 
cell. 



Fig. 268. 



the negative pole. This current may be controlled by 
a suitable resistance and measured by an ammeter. 
Storage cells have several advantages: (a) They can be 
charged and discharged a great many times before the 
material placed in the perforations in the plates falls out. 



CHEMICAL AND HEAT EFFECTS 



315 



(b) The electrical energy used in charging the plates 
costs less than the plates and electrolyte of voltaic cells. 

(c) Charging storage cells takes much less labor than 
replacing the electrolyte and plates of voltaic cells, (d) 
Storage cells produce larger currents than voltaic cells. 





Fig. 269. The Edison 
storage cell. 



Fig. 270. The plates of the Edison storage 
cell. 



The two principal disadvantages of storage cells are that 
(a) they are very heavy, and (b) their initial cost is 
considerable. 

289. The Edison storage cell (Figs. 269 and 270) has 
plates of iron and nickel oxide. The electrolyte is a 
strong solution of potassium hydroxide. These cells 



316 PHYSICS 

are lighter than lead cells of the same capacity and they 
are claimed to have a fonger life. 

290. Energy and Power of a Storage Cell. In a 
storage cell, the electrical energy of the charging current 
is transformed into chemical energy by the action of 
electrolysis. It is this chemical energy that is trans- 
formed into the energy of the electric current when the 
cell is discharged. The capacity of storage cells is rated 
in "ampere hours," a 40 ampere hour cell being capable 
of producing a current of 1 ampere for 40 hours, or 5 am- 
peres for 8 hours, etc. The production and extensive 
use of electric currents have made necessary accurate 
methods for measuring the energy and power of these 
currents. To illustrate how this is accomplished, let 
us imagine an electric circuit as represented in Fig. 268. 
Here four storage cells in series have an E.M.F. of 8 volts 
and in accordance with Ohm's law produce a current of 2 
amperes through a resistance in the circuit of 4 ohms. 
Now the work done or energy expended by the current in 
passing through the resistance between the points M and 
N depends upon three factors (1) the E.M.F. or potential 
difference; (2) the current intensity and (3) the time. The 
energy is measured by their product. That is, electrical 
energy = potential difference X current intensity X time. 
This represents the electrical energy in joules, or 

Joules = volts X amperes X seconds, or 
j = E X / X t. 

In the circuit represented in Fig. 268 the energy expended 
between the points M and N in 1 minute (60 seconds) is 
8 X 2 X 60 = 960 joules. 

291. Electric Power. Since power refers to the time 
rate at which work is done or energy expended, it may be 
computed by dividing the electrical energy by the time, 



CHEMICAL AND HEAT EFFECTS 317 

or the electrical power = volts X amperes. The power 
of 1 joule per second is called a watt. Therefore, 

Watts = volts X amperes, or 
Watts = EX I. 

Other units of power are the kilowatt = iooo watts 
and the horse-power = 746 watts. In the example given 
in Art. 290 the power of the current is 8 X 2 = 16 watts, 
or if the energy of the current expended between the 
joints M and N were converted into mechanical horse- 
power it would equal x %^ of a horse-power. Electrical 
energy is usually sold by the kilowatt-hour, or the amount 
of electrical energy that would exert a power of 1000 watts 
for one hour, or of 100 watts for 10 hours, or of 50 watts 
for 20 hours, etc. 

Important Topics 

1. The storage battery, its construction, electrolyte, action, uses, 
advantages, disadvantages. 

2. Electric energy, unit value, how computed? 

3. Electric power, three units, value, how computed, how sold? 



Exercises 

1. In what three respects are voltaic and storage cells alike? In 
what two ways different? 

2. Name the four advantages of storage cells in the order of their 
importance. Give your reasons for choosing this order. 

3. Why are dry cells more suitable for operating a door-bell circuit, 
than a storage battery? Give two reasons. 

4. The current for a city telephone system is provided by a storage 
battery. Why is this better than dry cells at each telephone? 

5. An incandescent lamp takes 0.5 ampere at no volts. What 
power is required to operate it? How much energy will it 
transform in 1 minute? 

6. How long would it take for this lamp to use a kilowatt hour of 
energy? 

7. A street car used 100 amperes at 600 volts pressure. What 



318 PHYSICS 

power was delivered to it? Express also in kilowatts and 
horsepower. 

8. An electric toaster takes 5 amperes at no volts. If it toasts 
a slice of bread in 2 minutes, what is the cost at 10 cents a 
kilowatt hour? 

9. An electric flat iron takes 5 amperes at no volts. Find the 
cost of using it for 2 hours at 12 cents a kilowatt hour. 

10. A Y kilowatt motor is used to run a washing-machine for 5 
hours. What is the expense for this power at 10 cents a kilo- 
watt hour? 

11. What is the efficiency of a motor that takes 7390 watts and 
develops 9 horse-power? 

12. How many horse-power are there in a water-fall 212 ft. high 
over which flows 800 cu. ft. of water per second? Express 
this power in kilowatts. 

13. What horse-power must be applied to a dynamo having an 
efficiency of 90 per cent, if it is to light 20 arc lamps in series, 
each taking 10 amperes at 60 volts? 

(3) The Heat Effect of Electric Currents 

292. The Production of Heat by an Electric Current. 

When no chemical or mechanical work is done by an elec- 
tric current its energy is employed in overcoming the resist- 
ance of the conducting circuit and is transformed into 
heat. This effect has many practical applications and some 
disadvantages. Many devices employ the heating effect 
of electric currents, (a) the electric furnace, (b) electric 
lights, (c) heating coils for street cars, (d) devices about 
the home, as flat irons, toasters, etc. Sometimes the 
heat produced by an electric current in the wires of a 
device such as a transformer is so large in amount that 
especial means of cooling are employed. Unusually 
heavy currents have been known to melt the conducting 
wires of circuits and electrical devices. Hence all circuits 
for electric power as well as many others that ordinarily 
carry small currents are protected by fuses. An electric 



CHEMICAL AND HEAT EFFECTS 



319 



fuse is a short piece of wire that will melt and break the cir- 
cuit if the current exceeds a determined value. The 
fuse wire is usually enclosed in an incombustible holder. 
Fuse wire is frequently made of lead or of an alloy of lead 
and other easily fusible metals. (See Figs. 271 and 272.) 
293. Heat Developed in a Conductor. A rule for com- 
puting the amount of heat produced in an electric circuit 
by a given current has been 
accurately determined by 
experiment. It has been 
found that 1 calorie of heat 
(Art. 142), is produced by 




Fig. 271. A type of enclosed fuse. 



Fig. 272. A link fuse (above); 
plug fuses (below). 



an expenditure of 4.2 joules of electrical (or other) energy. 
In other words, 1 joule will produce }.% or 0.24 calorie. 
Now the number of joules of electrical energy in an 
electric circuit is expressed by the following formula: 

Joules = volts X amperes X seconds, or since 1 joule 
= 0.24 calorie, 
Calories = volts X amperes X seconds X 0.24 or 

H = EI XtX 0.24 (1) 

By Ohm's law, /= ^or E = I X R, substituting in equa- 
tion (1) IR for its equal E we have 

H = PRXtX 0.24 (2) 

E E 

Also since I = ^ substitute ^ f or / in equation (/) and we 
K K 

have 



E 2 
H = ^tXo.24 



(3) 



320 



PHYSICS 



To illustrate the use of these formulas by a problem sup- 
pose that a current of 10 amperes is flowing in a circuit 
having a resistance of n ohms, for i minute. The heat 
produced will be by formula (2) = (10) 2 X 11 X 60 X 0.24 
equals 15,840 calories. 

294. The Incandescent Lamp. One of the most com- 
mon devices employing the heat effect of an electric cur- 
rent is the incandescent lamp. (See Fig. 273.) In this 
lamp the current is sent through a carbon filament, 





Fig. 273. A carbon filament 
incandescent lamp. 



Fig. 274. A tungsten 
lamp. 



which is heated to incandescence. In order to keep the 
filament from burning as well as to prevent loss of heat 
by convection, it is placed in a glass bulb from which the 
air is exhausted. Two platinum wires fused in the glass 
connect the carbon filament with the grooved rim and the 
end piece of the base. The end piece and rim connect with 
the socket so that an electric current may flow through the 
filament of the lamp. The carbon incandescent lamp has 
a low efficiency. It takes 0.5 ampere of current at no 
volts or in other words it requires 55 watts to cause a 16- 



CHEMICAL AND HEAT EFFECTS 



321 



candle-power lamp to glow brightly, hence 1 candle 
power in this lamp takes 55 * 16 = 3.43 watts. 

The efficiency of electric lamps is measured by the num- 
ber of watts per candle power. This is a peculiar use of the 
term efficiency, as the larger the number the less efficient 
is the lamp. More efficient lamps have been devised with 
filaments of the metals tantalum and tungsten (Fig. 274). 
These give a whiter light than do carbon lamps, and con- 
sume but about 1.25 watts per candle power. 



Comparative "Efficiency" of Electric Lamps 



Name of lamp 



Watts per 
candle Name of lamp 
power 



Watts per 
candle 
power 



Carbon filament. . 
Metallized carbon 

Tantalum 

Tungsten 



3 to 4 

2.5 

2.0 

1.0 to 1.5 



Arc lamp 
Mercury arc 
Flaming arc 
Nitrogen-filled 
tungsten 



0.5 to 0.8 

0.6 

0.4 
0.6 to 0.7 



Incandescent lamps are connected in parallel (see Fig. 
254) to wires that are kept at a constant difference of 
potential of no or 115 volts. It is customary to place 
not more than twelve lamps upon one circuit, each circuit 
being protected by a fuse and controlled by one or more 
switches. 

295. The Arc Light. The electric arc light (see Fig. 
275) is extensively used for lighting large rooms, also in 
stereopticons and motion picture machines. The light is 
intense, varying from 500 to 1700 candle power. The so- 
called mean spherical candle power of the arc light is about 
510. The candle power in the direction of greatest inten- 
sity is about 1200. It is produced at an expenditure of 
21 



322 



PHYSICS 



about 500 watts. It is therefore more efficient than the 
incandescent lamp, often taking less than 0.5 watt per 
candle power produced. The arc light was first devised by 
Sir Humphrey Davy in 1809, who used two pieces of char- 
coal connected to 2000 voltaic cells. The arc light re- 
quires so much power that its production by voltaic cells is 
very expensive. Consequently it did not come into com- 
mon use until the dynamo had been perfected. Fig. 276 





Fig. 275. An electric axe light. 



Fig. 276. The ap- 
pearance of a pair of 
used carbons. 



shows the appearance of the two carbons in an arc light. 
If a direct current is used the positive carbon is heated 
more intensely, and gives out the greater part of the light. 
The positive carbon is consumed about twice as fast as the 
negative and its end is concave, the negative remaining 
pointed. 

With alternating currents, the rods are equally con- 
sumed and produce equal amounts of light. In the stere- 
opticon, the carbons are usually placed at right angles as 



CHEMICAL AND HEAT EFFECTS 



323 



in Fig. 277. In the stereopticon as well as in outdoor 
lighting the direct current is more effective, although the 
alternating current is often used, since the latter can be 
produced and distributed more cheaply than can direct 
currents. In arc lamps, placing an inner glass globe 
(Fig. 278) about the carbons, decreases the consumption 
of the carbons materially. The carbon rods of enclosed 
arc lamps often last 60 to 100 hours. 





Fig. 277. A right-angle electric 
arc lamp for a stereopticon. 



Fig. 278. An enclosed 
arc lamp. 



The reason why an open arc lamp needs to be " retrimmed " oftener 
than the enclosed lamp, that is, have new carbons placed in it, 
is because the carbons "burn" freely, that is unite with the oxygen 
of the air. In the enclosed arc lamp, the supply of oxygen in the 
inner globe is limited and is soon consumed, therefore the carbons 
last many times longer in such lamps. 



Some carbon rods have soft cores containing calcium 
salts. These vaporize in the arc producing the flaming arc 
light of a bright yellow color, and give more light than 
the ordinary lamp. 

Important Topics 

1. Heat effects of electric currents, uses and applications. 

2. Computation of the heat developed in a circuit. Three formulas. 

3. Electric lamps; incandescent and arc; construction, uses, effi- 
ciency. 



324 PHYSICS 



Exercises 



i. Sketch a circuit containing 10 incandescent lamps in parallel. 
If each lamp when hot has a resistance of 220 ohms, and the 
E.M.F. is 100 volts, what current will flow? 

2. What will it cost to use these lights for 3 hours a day for 30 
days at 10 cents a kilowatt hour? 

3. How much heat will these lamps produce per minute? 

4. How could you connect no-volt lamps to a street car circuit 
of 660 volts? Explain this arrangement and draw a diagram. 

5. A certain arc lamp required 10 amperes of current at 45 volts 
pressure. What would it cost at 10 cents per kilowatt hour 
if used 3 hours a day for 30 days? 

6. Show a diagram of 3 arc lamps in series. If each takes 45 volts 
and 10 amperes, how much E.M.F. and current will they 
require? 

7. If an electric toaster uses 5 amperes at 115 vofts, how much 
heat will this develop in half an hour? 

9. How much heat is developed in an electric toaster in 2 minutes, 
if it uses 5 amperes at 100 volts? 

10. How many B.t.u.'s are given off in an electric oven that takes 
10 amperes at no volts for 1 hour? (1 B.t.u. equals 252 
calories.) 

11. An electric heater supplies heat at the rate of 700 B.t u.'san 
hour. How much power does it require? 

12. How many watts are required to operate 120 incandescent 
lamps in parallel if each takes 0.5 amperes at no volts? 

13. An electric lamp takes 12 amperes at a P.D. of no volts. 
How many B.t.u.'s are radiated from it each second? How 
many calories? 

14. If a 1 10- volt incandescent lamp is submerged for 10 minutes in 
400 gr. of cold water while a current of 0.5 amperes is flowing, 
how many degrees centigrade will the water be warmed? 

15. In an electric furnace a current of 3000 amperes is used at 
a P.D. of 10 volts. Find the heat developed in 1 minute. 

16. How many candle power should a 20-watt tungsten lamp give 
if its efficiency is one watt per candle power? 

17. What is the " efficiency " of a 40-watt tungsten lamp if it gives 
34 candle power? 



CHEMICAL AND HEAT EFFECTS 325 

Review Outline: Current Electricity 

Produced by Chemical action ; voltaic and storage cells. 

Three [ Magnetic, electromagnet, uses and applications. 

Principal Chemical, electrolysis, applications. 

Effects : [ Heat, -lighting and heating devices. 

Theories: (a) of voltaic cells, (b) of electrolysis. 

Units,: Ampere, ohm, volt, watt, joule, kilowatt, horse power. 

Measurement (a) magnetic effect; galvanometer, ammeter, volt- 
meter, wattmeter, Wheatstone bridge, con- 
struction and use. 
(b) chemical effect; voltameter. 

Laws: (a) Right hand rules, for conductor and helix. 

(b) Resistance, Conductors in series and parallel. 

(c) Ohm's law, heat law, power law, 3 forms for 
each. 

(d) Cells in parallel and series. 

Problems: Upon applications of the laws and formulas studied. 
' Voltaic cells; wet, dry, and Daniell. 
Electrolysis and the storage battery. 
Measuring instruments, electric bell, sounder. 
, heating and lighting devices. 
Terms: Anode, cathode, electrolyte, ion, circuit switch, current, 
e.m.f., resistance, potential. 



Devices 

and 

Instruments 



CHAPTER XIV 
INDUCED CURRENTS 

(i) Electromagnetic Induction 

296. Current Induced by a Magnet. The discovery 
in 1819 that a current in a conductor can deflect a magnetic 
needle or that it has a magnetic effect, led to many at- 
tempts to produce an electric current by means of a magnet. 
It was not until about 1831, however, that Joseph Henry 
in America and Michael Faraday in England, ind pen- 
dently discovered how to accomplish this important result. 

At the present time, voltaic cells produce but a very 
small part of the current electricity used. Practically all 
that is employed for power, light, heat, and electrolysis is 
produced by the use of magnetic fields, or by electromag- 
netic induction. 

297. Laws of Induced Currents. ' To illustrate how a 
current can be produced by electromagnetic induction: 

Connect a coil of 400 or more turns of No. 22 insulated copper 
wire to a sensitive galvanometer. (See Fig. 279.) Now insert a 
bar magnet in the coil. A sudden movement of the galvanometer 
will be noticed, indicating the production of a current. When the 
magnet stops moving, however, the current stops, and the coil of 
the galvanometer returns to its first position. If now the magnet 
is removed, a movement of the galvanometer coil in the opposite 
direction is noticed. This action may be repeated as often as de- 
sired with similar results. 

Careful experiments have shown that it is the magnetic 
field of the magnet that produces the action, and that 

x An induced current is one produced by changing the number of 
magnetic lines of force passing through a coil. 

326 



INDUCED CURRENTS 



327 



only when the number of lines of force in the coil is changing 
do we find a current produced in the coil. These facts 
lead to Law I. Any change in the number of magnetic 
lines of force passing through or cut by a coil will produce an 
electromotive force in the coil. In the account of the experi- 
ment just given, electric currents are produced, while in 
Law I, electromotive forces are mentioned. This difference 
is due to the fact that an E.M.F. is always produced in a 




I illlllh 

H- ifKnltltftTtWlOT 



111"! '1! 1'!' I,'" 
/' /////' /"'/' "'''' '' 



Fig. 279. The moving mag- 
net induces a current in the 
coil. 



Fig. 280. A current may be in- 
duced by turning the coil in the 
earth's magnetic field. 



coil when the magnetic field within it is changed, while a 
current is found only when the coil is part of a closed 
circuit. The inductive action of the earth's magnetic field 
(see Fig. 280), may be shown by means of a coil of 400 to 
500 turns a foot in diameter. 

Connect its ends to a sensitive galvanometer and hold it at right 
angles to the earth's field. Then quickly revolve the coil through 
180 degrees and note the movement of the galvanometer. Reverse 
the coil and the galvanometer swings in the opposite direction. 

If the magnet in Fig. 279 is moved in and out of the 
coil at first slowly and later swiftly, small and large deflec- 
tions of the galvanometer coil are noticed. The quicker 
the movement of the magnetic field the greater are the 
galvanometer deflections produced. This leads to Law II. 



328 



PHYSICE 



The electromotive forces produced are proportional to the 
number of lines of force cut per second. 

298. The magneto is a device that illustrates the laws 
of induced currents stated in Art. 297. The magneto 
(see Fig. 281), consists of several permanent, "U"-shaped 
magnets placed side by side. Between the poles of these 
magnets is placed a slotted iron cylinder having a coil of 
many turns of fine insulated copper wire wound in the 
slot as in Fig. 282. The cylinder and coil form what is 




Fig. 281. A magneto. 



Fig. 282. A shuttle armature. 



called an armature. The armature is mounted so as to 
be revolved between the poles of the "U"-shaped magnets 
by means of a handle. As the armature revolves, the 
lines of force from the magnets pass through the coil first 
in one direction and then in the other. This repeated 
change in the lines of force passing through the coil pro- 
duces an E.M.F. which may be felt by holding in the hands 
the two wires leading from the armature coil. On turn- 
ing the armature faster the current is felt much strouger, 
showing that the E.M.F. in the coil increases as the rate 
of cutting the magnetic lines of force by the coils increases. 
299. Lenz's Law. While one is turning the armature 
of a magneto if the two wires leading from its coil are 
connected, forming what is called a "short circuit," the 
difficulty of turning the armature is at once increased. 
If now the circuit is broken, the armature turns as easily 



INDUCED CURRENTS 



329 



as at first. The increased difficulty in turning the arma- 
ture is due to the current produced in the coil. This cur- 
rent sets up a magnetic field of its own that opposes 
the field from the steel magnets. This opposition makes 
it necessary for work to be done to keep up the motion 
of the coil when a current is passing through it. This 
fact is called Lenz's Law. It may be expressed as follows : 
Whenever a current is induced by the relative motion of a 
magnetic field and a conductor, the direction of the induced 
current is always such as to set up a magnetic field that 



$ Wn W 





mN < 



Fig. 283. The induced current has a field which opposes the motion of 
the magnet. The heavy line represents the direction of the induced 
current. 

opposes the motion. Lenz's Law follows from the principle 
of conservation of energy, that energy can be produced 
only from an expenditure of other energy. Now since an 
electric current possesses energy, such a current can be 
produced only by doing mechanical work or by expending 
some other form of energy. To illustrate Lenz's Law, 
suppose that the north-seeking pole of a bar magnet be 
inserted in a closed coil of wire. (See Fig. 283.) The 
current induced in the coil has a direction such that its lines 



33 PHYSICS 

of force will pass within the coil so as to oppose the field 
of the bar magnet, when the north pole of the magnet is 
inserted so as to point to the left. That is, the north pole 
of the helix is at the right. Applying the right-hand rule 
to the coil, its current will then be counter clockwise. On 
withdrawing the magnet, the current reverses, becoming 
clockwise with its field passing to the left within the coil. 
A striking illustration of the opposition offered by the 
field of the induced current to that of the inducing field 
is afforded by taking a strong electro magnet (see Fig. 
284) and suspending a sheet of copper so ' 
as to swing freely between the poles. 
When no current flows through the mag- 
net the sheet swings easily for some 
time. When, however, the coils are 
magnetized, the copper sheet has induced 
within it, currents that set up magnetic 
fields strongly opposing the motion, the 
swinging being stopped almost instantly. 
Fig. 284. The The principle is applied in good amme- 
sto* s theswin^n 1 ters anc ^ voltmeters to prevent the swing- 
of the sheet of ing of the needle when deflected. The 
current induced in. the metal form on 
which is wound the galvanometer coil is sufficient to make 
the needle practically "dead beat." 

300. The Magneto and the Dynamo. Magnetos are 
used to develop small currents,- such as are used for tele- 
phone signals, and for operating the sparking devices of 
gasoline engines. They are therefore found in automo- 
biles containing gasoline motors. The most important 
device for producing electric currents by electromagnetic 
induction, however, is the dynamo. It is employed when- 
ever large currents are desired. The principle of this 
device is similar to that of the magneto except that it con- 




Lord Kelvin (Sir William Thom- 
son), (1824-1907). Professor of 
Physics, Glasgow University. In- 
vented the absolute scale of tem- 
perature: also many practical 
electrical measuring instruments. 
The foremost physicist of the latter 
part of the nineteenth century. 





Lord Kelvin 
By Permission of the Berlin Photo- 
graphic Co., New York." 



Michael Faraday (1 791-1867). 
Famous English Physicist. Made 
many discoveries in electricity 
and magnetism; "Greatest ex- 
perimentalist of the nineteenth 
century." 



Michael Faraday 
" By Permission of the Berlin Photo- 
graphic Co., New York." 



INDUCED CURRENTS 



333 



tains an electromagnet for producing the magnetic field. 
Since the electromagnet can develop a much stronger field 
than a permanent magnet, the dynamo can produce 
a higher E.M.F. and a much larger current than the 
magneto. 

301. The Magnetic Fields of Generators. In the 
magneto, the magnetic field is produced by permanent steel 
magnets. In dynamos powerful electromagnets are used. 



Main Circuit 



MainCfrtait 

22" 



MarnCfrcait 





Fig. 285. A series- 
wound dynamo. 



Fig. 286. A shunt- 
wound dynamo. 



Fig. 287. A compound- 
wound dynamo. 



The latter are sometimes excited by currents from some 
other source, but usually current from the armature is 
sent around the field coils to produce the magnetic fields. 
Dynamos are classified according to the manner in which 
the current is sent to their field coils. 

A. The series wound dynamo (see Fig. 285) is arranged 
so that all of the current produced by the armature is sent 
through coils of coarse wire upon the fields, after flowing 
through the external circuit. 

B. The shunt wound dynamo (see Fig. 286) sends a 
part only of the current produced through the field coils. 
The latter are of many turns of fine wire so as to use as 
little current as possible. The greater part of the current 
goes to the main circuit. If the number of lamps or motors 



334 physics 

connected to the main circuit is increased, the voltage is 
lessened which weakens the current in the field coils, 
causing a weaker field and still lower voltage, producing a 
fluctuating E.M.F. which is unsatisfactory for many 
purposes. This fault is overcome by 

C. the compound wound dynamo. This dynamo has 
both shunt and series coils upon its fields. (See Fig. 287.) 
If more current is drawn into the main circuit with this 
dynamo, the series coils produce a stronger field compen- 
sating for the weaker field of the shunt coils, so that 
uniform voltage is maintained. The compound wound 
generator is therefore the one most commonly employed. 

Important Topics 

1. Laws of electromagnetic induction (a) conditions, (b) E.M.F., 
(c) direction. . 

2. Devices, (a) magneto, (b) dynamo: series, shunt, compound. 

3. Illustrations of the laws. 

Exercises 

1. Under what conditions may an electric current be produced 
by a magnet? 

2. Show how Lenz's Law, follows from the principle of conserva- 
tion of energy. 

3. A bar magnet is fixed upright with its north-seeking pole up- 
ward. A coil is thrust down over the magnet. What is the 
direction of the current induced in the coil? Explain. 

4. In what two ways may a current be induced in a closed coil? 

5. What method is employed in the magneto? In the dynamo? 

6. What is the nature of the current produced in the armature 
coil of a magneto, that is, is it direct or alternating? Why? 

7. What is the resistance of a 20-watt tungsten lamp if the E.M.F. 
is 115 volts? 

8. Find the resistance of a 40-watt tungsten lamp when the 
voltage is 115? How much heat will it produce per minute? 

9. An Edison storage battery cell on a test gave a discharge of 
30 amperes. The average voltage was 1.19. What was the 
resistance of the cell? 



INDUCED CURRENTS 



335 



io. Eight storage cells are connected in series. Each has an E.M.F. 
of 1.2 volts and an internal resistance of 0.03 ohms. What will 
be the current flowing through a voltmeter having 500 ohms 
resistance in circuit with them? 

(2) The Dynamo and the Motor 

302. The Dynamo may be defined as a machine for 
transforming mechanical energy into the energy of electric 
currents by electromagnetic induction. Although elec- 



g 



1 

Fig. 2? 









. Several methods of arranging the field coils and the armature 
of a dynamo. 



tromagnetic induction was discovered in 1821, practical 

dynamos were not built for about 40 years or until between 

i860 and 1870. The great development in the production 

and use of electric currents has come since the latter date. 

The principle parts of the dynamo are (a) the field magnet, 

(b) the armature, (c) the 

commutator or collecting Jummmm^^s^ 

rings, (d) the brushes. 

Fig. 288 shows several 

common methods of 

arranging the field coils 

and the armature. 

The field coils vary in number and position. The 
purpose of their construction is always to send the largest 
possible number of lines of force through the armature. 
Some dynamos are bipolar, or have two poles, others are 
multipolar or have more than two. In Fig. 288 No. 4 
has four poles. The armature of a dynamo differs from a 
magneto armature in that it consists of a series of coils of 




Fig. 289. A drum armature. 



336 PHYSICS 

insulated copper wire wound in numerous slots cut in the 
surface of a cylindrical piece of iron. Fig. 289 shows a 
side view of the iron core of such an armature. Iron is 
used to form the body of the armature since the magnetic 
lines of force flow easily through the iron. The iron by its 
permeability also concentrates and increases the magnetic 
flux. The best armatures are made of many thin sheets 
of soft iron. These are called laminated armatures. An 
armature made of a solid piece of iron becomes hot when 
revolving in a magnetic field. This is due to electric 
currents induced in the iron itself. This heating is 
largely reduced by laminating the armature. Why? 

303 . Methods of Collecting Current from the Armature . 
The electric currents produced in the armature are 
conducted away by special sliding contacts'. The sta- 
tionary part of the sliding contact is called a brush. The 



Fig. 290. Armature connected to slip rings producing an alternating 

current. 

moving part is a slip ring or a commutator. Fig. 290 shows 
an armature coil connected to slip rings. As the armature 
revolves, the coils and slip rings revolve with it. The two 
ends of the armature coils are connected to the two rings 
respectively. Now as the armature revolves it cuts the 
lines of force first in one direction and then in the other. 
This produces in the coils an E.M.F. first one way and then 
the other. This E.M.F. sets up a current which is con- 
ducted to the outside circuits through the slip rings and 



INDUCED CURRENTS 



337 




brushes. Such a current which repeatedly reverses its 
direction is called an alternating current. Fig. 291 (1) in- 
dicates graphically how the current moves alternately 
one way and then the other. Alternating currents are 
extensively used for electric light, heat, and power. Direct 
currents or those going continuously in one direction are 
however in much demand especially for street car service, 
for electrolysis, and for charging storage batteries. 

304. The Commutator. For a dynamo to deliver a 
direct current it must carry upon the shaft of the armature 
a commutator. The 
commutator is used 
to reverse the con- 
nections of the ends 
of the armature coils 
at the instant that 
the current changes 
its direction in the 
armature. This reversal of connection when the direc- 
tion of current changes, keeps the current in the outside 
circuit flowing in the same direction. Fig. 291 is a dia- 
gram of an armature with a commutator. The commu- 
tator is a split ring, having as many parts or segments as 
there are coils upon the armature. The brushes touch 
opposite points upon the commutator as they slide over 
the surface of the latter. Suppose that the armature 
viewed from the commutator end rotates in a counter- 
clockwise direction, also that the currents from the upper 
part move toward the commutator and out the top brush. 

As the armature revolves, its coils soon begin to cut 

the force lines in the opposite direction. This change in 

the direction of cutting the lines of force causes the current 

to reverse in the coils of the armature. At the instant the 

current changes in direction, what was the upper segment 
22 



Fig. 291. The armature coils are connected 
to a commutator producing a direct current. 



33 



PHYSICS 



0), 




of the commutator slips over into contact with the lower 
brush, and the other segment swings over to touch the 
upper brush. Since the current has reversed in the coils 

it continues to flow out of the 
upper brush. This change in 
connection at the brushes takes 
place at each half turn of the 
armature, just as the current 
changes in direction in the coils. 
This is the manner in which 
Fig. 292. Graphic represen- t h e commutator of a dynamo 

tation of (1) an alternating , * 

current; (2) a pulsating current; changes the alternating current 
(3) a continuous current. produce d in the armature coils, 

into a direct current in the external circuit. .Fig. 292 (1) 
represents graphically an alternating current, (2) of the 



0/~\r\r\^\ 




Fig. 293. DeLaval multi-stage turbine and gear driving 750-kw., 750- 
r.p.m., 600-volt direct-current generator. 

same figure shows current taken from the brushes 
of the commutator of a dynamo with one coil on the 
armature. 

A practical dynamo, however, has many coils upon its 



INDUCED CURRENTS 



339 



armature with a corresponding number of segments upon 
the commutator. (See Figs. 289 and 293.) As each coil 
and commutator segment passes a brush, it contributes 
an impulse to the current with the result that armatures 
with many coils produce currents that flow quite evenly. 
(See Fig. 292, 3.) 

The current represented in Fig. 292 (2) is called a pul- 
sating current. 

305. The electric motor is a machine which transforms 
the energy of an electric current into mechanical energy 
or motion. The direct current motor consists of the same 




Fig. 294. 



-A wire carrying a current across a magnetic field is pushed 
sideways by the field. 



essential parts as a direct current dynamo, viz., the field 
magnet, armature, commutator and brushes. Its opera- 
tion is readily comprehended after one understands the 
following experiment: 

Set up two bar electromagnets with unlike poles facing 
each other about an inch apart. A wire connected to a 
source of current is hung loosely between the poles as in 
Fig. 294. The circuit through the wire should contain a 
key or switch. If a current is sent through the electro- 
magnets and then another is sent through the wire, the 



34 



PHYSICS 



latter will be found to be pushed either up or down, while 
if the current is reversed through the wire it is pushed in 
the opposite direction. These results may be explained 
as follows: 

Consider the magnetic field about a wire carrying a cur- 




N 



Fig. 295. The mag- 
netic field about a wire 
carrying a current. 



Fig. 296. The magnetic field be- 
tween two unlike poles. 



rent. (See Fig. 295.) If such a wire is placed in the mag- 
netic field between two opposite poles of an electromagnet 
(Fig. 296), the wire will be moved either up or down. 
The reason for this is shown by the diagram in Fig. 297. 
Here a wire carrying a current and therefore surrounded 

by a magnetic field passes 
across another magnetic 
field. The two fields 
affect each other causing 
a crowding of the force 
lines either above or below 

Fig. 297 The crowding of the lines the wire. The wire at 
of force above the wire, pushes it once ten( J s to mo V e side- 
downward. 

ways across the field away 

from the crowded side. In the figure, the wire tends to 

move downward. 

In a practical motor, the wires upon the armature are 

so connected that those upon one side (see Fig. 298), carry 

currents that pass in, while on the other side they pass out. 

To represent the direction of the current in the wires, the 




INDUCED CURRENTS 



341 




Fig. 298. The crowding of the lines 
of force causes the armature to revolve 
in a clockwise direction. 



following device is employed; a circle with a cross (to 
represent the feather in the tail of an arrow) indicates a 
current going away from the observer, while a circle with 
a dot at its center (to 
represent the tip of an 
arrow) indicates a cur- 
rent coming toward the 
observer. 

In Fig. 298 the north 
pole is at the left and 
the south pole at the 
right. The field of the magnets therefore passes from 
left to right as indicated in the figure. Now in the arma- 
ture the currents in the wires on the left half of the arma- 
ture are coming toward the observer while those on the 

right move away. 
Applying the right- 
hand rule, the mag- 
netic lines will crowd 
under the wires on 
the left side of the 
armature while they 
will crowd over the 
wires on the right 
side. This will cause 
a rotation up on the 
left side and down 
on the right, or in 
a clockwise direction. 
If the current in 
the armature is re- 
versed (in on the left and out on the right), the lines of 
force will crowd the armature around in the opposite 
direction or counter clockwise. The rotation of the 




Fig. 299. 



-View of a one-half horse-power 
motor. 



342 



PHYSICS 



armature will also be reversed if, while the current in the 
armature is unchanged in direction, the poles of the 
magnet are changed thus reversing the magnetic field. 

The motorman of a street car reverses the motion of 
his car by reversing the direction of the current in the 
armature of the motor. 




Fig. 300. The frame and electromagnet (at left), front bracket and 
brush holder (at right) of the motor shown in Fig. 299. 




Fig. 301. The armature of a motor. 

306. Practical motors have many coils upon the arma- 
ture with a corresponding number of segments upon the 
commutator. A large number of coils and commutator 
segments enables some one of the coils to exert its greatest 
efficiency at each instant, hence a steady force is provided 
for turning the armature which causes it to run smoothly. 



INDUCED CURRENTS 343 

Fig. 299 represents a ^ horse-power motor ready for use 
while Fig. 300 shows the frame and poles and the front 
bracket and brush holder, and Fig. 301 represents the 
armature. 

Important Topics 

1. The dynamo, four essential parts, action (a) for alternating 
currents, (b) for direct currents. 

2. The electric motor: (a) essential parts, (b) action. 

Exercises 

1. Why is an alternating current produced in the armature of a 
dynamo? 

2. Row is this current produced? Give careful explanations. 

3. What is the result of Lenz's law as applied to the dynamo? 

4. Apply the first two laws of electromagnetic induction to the 
dynamo. 

5. What is the power of a dynamo if it produces 40 amperes of cur- 
rent at no volts? 

6. How much power must be applied to this dynamo if its efficiency 
is 90 per cent. ? 

7. A motor takes 10 amperes of current at 220 volts; what is the 
power of the current in watts? If this motor has an efficiency 
of 95 per cent., how many horse-power of mechanical energy 
can it develop? 

8. Explain why reversing the current in the armature of a motor 
reverses the direction of rotation. 

9. Find the cost of running a washing machine using a ^-horse- 
power motor 2 hours if the cost of the electricity is 10 cents 
a kilowatt hour. 

10. A >^-horse-power motor is used to run a sewing machine. 
If used for 3 hours what will be the cost at n cents a kilowatt 
hour? 

(3) The Induction Coil and the Transformer 

307. The Induction Coil. Practically all electric cur- 
rents are produced either by voltaic cells or by dynamos. 
It is frequently found, however, that it is desirable to 



344 



PHYSICS 




Fig. 302. An induction coil. 



change the E.M.F. of the current used, either for purposes 
of effectiveness, convenience, or economy. The induction 
coil and the transformer, devices for changing the E.M.F. 
of electric currents, are therefore in common use. The 
induction coil (see Fig. 302) consists of a primary coil of 
coarse wire P (Fig. 303) wound upon a core of soft iron 

wire, and a secondary coil, 
S, of several thousand 
turns of fine wire. In 
circuit with the primary 
coil is a- battery, B, and a 
current interrupter, K, 
which works iike the in- 
terrupter upon an electric 
bell. The ends of the secondary coil are 'brought to 
binding posts or spark points as at D. 

The current from the battery flows through the primary 
coil magnetizing the iron core. The magnetism in the 
core attracts the soft-iron end of the interrupter, drawing 
the latter over and breaking the circuit at the screw con- 
tact, K. This abruptly 
stops the current and at 
onee the core loses its 
magnetism. The spring 
support of the inter- 
rupter now draws the 
latter back to the con- 
tact, T, again complet- 
ing the circuit. The 
whole operation is re- 
peated, the interrupter vibrating rapidly continually open- 
ing and closing the circuit. 

308. The Production of Induced Currents in the 
Secondary Coil. When the current flows through the 




Fig. 



303. Diagram showing the parts of 
an induction coil. 



INDUCED CURRENTS 345 

primary it sets up a magnetic field in the core. When 
the current is interrupted, the field disappears. The in- 
crease and decrease in the field of the core induces an 
E.M.F. in the secondary coil, in accordance with the first 
law of electromagnetic induction. The E.M.F. produced 
depends upon (a) the number of turns in the secondary, 
(b) the strength of the magnetic field and (c) the rate of 
change of the field. The rate of change in the field is 
more rapid at the break than at the make. When the 
circuit is closed it takes perhaps }{ o of a second for the 
current to build up to its full strength while at a break 
the current stops in perhaps o.ooooi of a second, so that 
the induced E.M.F. is perhaps 10,000 times as great at 
"break" as at make. To increase the suddenness of the 
"make" and "break," a condenser is often connected in 
the primary circuit, in parallel, with the interrupter. (See 
Fig. 303, C.) This condenser provides a place to hold the 
rush of current at the instant that the interrupter breaks 
the circuit. This stored up charge reinforces the current 
at the make producing a much more sudden change in the 
magnetic field with a corresponding increase in the E.M.F. 
The induced currents from induction coils are sometimes 
called faradic currents in honor of Faraday who discovered 
electromagnetic induction. They are used to operate 
sparking devices upon gas and gasoline engines and in 
many devices and experiments in which high-tension 
electricity is employed. 

309. The Transformer. This is like the induction coil 
in that it uses a primary and a secondary coil, and an iron 
core to carry the magnetic field. (See Fig. 304.) They 
differ in that the transformer has a closed core or one form- 
ing a continuous iron circuit, while the induction coil has 
an open core, or one in which the magnetic field must travel 
in air from the north to the south poles of the core. The 



346 



PHYSICS 



transformer must always be used with an alternating cur- 
rent while the induction coil may use either a direct or an 
alternating current. Further, the induction coil always 
produces a higher E.M.F. while the transformer may pro- 





Fig. 304. The transformer has a closed core; the induction coil, an open 

core. 



duce an E.M.F. in its secondary coil that is either higher or 
lower than the one in the primary. The former is called 
" step-up" while the latter is a "step-down" transformer. 
The alternating current in the primary coil of the trans- 
former produces an alternating magnetic flux in the iron 





305. The laminated iron core 
of a transformer. 



Fig. 306. Cross-section of 
the transformer shown in Fig. 
305 showing the magnetic field 
around the primary and sec- 
ondary coils. 



core. This iron core is laminated (see Fig. 305) to prevent 
the heating that would result if a solid core were used. 
The alternating magnetic flux induces in the secondary 
coil an E.M.F. in accordance with the following rule. The 




INDUCED CURRENTS 347 

ratio of the number of turns in the primary to the number 
of the turns in the secondary coil equals the ratio of the 
electromotive forces in these respective coils. If the 
secondary coil has 8 turns while the primary has 4, the 
E.M.F. of the secondary will be just twice that of the pri- 
mary. Or, if in the primary coil of the transformer Fig. 
306 is an E.M.F. of no volts, in the secondary will be 
found an E.M.F. of 220 volts. 

310. Uses of Transformers. In electric lighting sys- 
tems, dynamos often produce alternating currents at 
1000 to 12,000 volts pressure. It is very 
dangerous to admit currents at this pres- 
sure into dwellings and business houses, 
so that transformers are installed just 
outside of buildings to " step-down" the 
high voltage currents to no or 220 volts. 

The lighting current that enters a house FlG A 

does not come directly from a dynamo, commercial trans- 
It is an induced current produced by a 
transformer placed near the house. (See Fig. 307.) In 
a perfect transformer the efficiency would be 100 per 
cent. This signifies that the energy that is sent into the 
primary coil of the transformer exactly equals the energy 
in the secondary coil. The best transformers actually 
show efficiencies better than 97 per cent. The lost energy 
appears as heat in the transformer. " The transfer of 
great power in a large transformer from one circuit to 
another circuit entirely separate and distinct, without any 
motion or noise and almost without loss, is one of the 
most wonderful phenomena under the control of man." 

311. The mercury arc rectifier is a device for changing 
an alternating current into a direct current. It is fre- 
quently used for charging storage batteries where only 
alternating current is supplied by the electric power com- 



348 



PHYSICS 



JVWWWWWWVU 



pany. It consists of an exhausted bulb containing two 
carbon or graphite electrodes marked G in Fig. 308 and a 
mercury electrode marked M . It is found that current 

will pass through such a 
bulb only from the graph- 
ite to the mercury but not 
in the reverse direction. 
In operating the device, 
the secondary terminals of 
an alternating current 
transformer T are con- 
nected to the graphite 
terminals of the rectifier. 
A wire connected to the 
center of the secondary 
of the transformer at C is 
attached to the negative 
terminal of the storage 
mercury battery SB. The positive 
, terminal of the battery is 
connected to the mercury electrode of the rectifier tube 
through a reactance or choke coil R. This coil serves to 
sustain the arc between the alternations. Sw is a starting 
switch, used only in striking the arc. It is opened imme- 
diately after the tube begins to glow. 




Fig. 308. 



-Diagram of 
arc rectifier. 



Important Topics 

Transformer, induction coil, mercury are rectifier, construction, 
action; uses of each. 

Exercises 

1. Does the spark of an induction coil occur at "make" or a 
"break?" Why? 

2. What must be the relative number of turns upon the primary 
and secondary coils of a transformer if it receives current at 



INDUCED CURRENTS 349 

220 volts and delivers current at no? Also show by diagram. 

3. Would the transformer work upon a direct current? Why? 

4. Explain why the interrupter is a necessary part of the induction 
coil and not of the transformer. 

5. If a building used eighty no- volt incandescent lamps, what 
E.M.F. would be necessary to light them if they were joined 
in series? Why would this not be practical? 

6. If a 16-candle-power lamp requires 0.5 ampere upon a no-volt 
circuit what current and voltage will be needed to operate 12 
such lamps in parallel? 

7. What will it cost to run these lamps 4 hours a night for 30 days 
at 10 cents per kilowatt hour? 

8. If a mercury arc rectifier uses 5 amperes of current at no volts 
alternating current to produce 5 amperes of direct current at 70 
volts, what is the efficiency of the rectifier? 

9. Compute the heat produced in a 40 watt tungsten lamp in 
1 minute. 

10. Compute the heat produced in a 60 watt carbon incandescent 
lamp in 1 hour. 

(4) The Telephone 

312. The Electric Telephone. This is an instrument 
for reproducing the human voice at a distance by an elec- 
tric current. The modern electric telephone consists of 
at least four distinct parts (see Fig. 312) ; viz., a transmitter, 
an induction coil, an electric battery, and a receiver. The 
first three of these are concerned in sending, or transmitting 
over the connecting wires a fluctuating electric current, 
which has been modified by the waves of a human voice. 
The receiver, is affected by the fluctuating current and 
reproduces the voice. It will be considered first, in our 
study. 

313. The telephone receiver was invented in 1876 by 
Alexander Graham Bell. It consists of a permanent steel 
magnet, U shaped, with a coil of fine insulated copper wire 
about each pole. (See Fig. 310.) A disc of thin sheet 
iron is supported so that its center does not quite touch the 



35 



PHYSICS 




Fig. 309. The simplest telephone 
system. It consists of two telephone 
receivers connected in series on a cir- 
cuit. It will work, but not satisfac- 
torily. 



poles of the magnet. A hard rubber cap or ear piece with 
an opening at its center is screwed on so as to hold the 
iron disc firmly in place. 

The action of the receiver may be understood from the 
following explanation: The electric current sent to the 

receiver, comes from the 
secondary coil of the in- 
duction coil; it is an 
alternating current, fluc- 
tuating back and forth 
just in time with the 
waves of the voice affect- 
ing it at the transmitter. 
This alternating current flows around the coils on the 
poles of the permanent magnet. When this current 
flows in one direction, its magnetic field assists the 
field of the permanent magnet, strengthening it. This 
stronger magnetic field draws the thin iron disc in front 
of the poles of the magnet a little closer to them. When 
the current in the coils flows the other way, its magnetic 
field weakens the field of the steel magnet, and the disc is 
drawn back by the force of its own elasticity. Thus the 
disc of the receiver vibrates with the alternations of the 
current, and reproduces the same 
sounds that were spoken into the G\ 
transmitter. - 

314. The Telephone Trans- 
mitter. The telephone receiver FlG 3I0 ._ A telephone 

just described has great sensitive- receiver. This receiver has 

. . a permanent horseshoe mag- 

neSS in reproducing SOUnd, but it net with a coil about each 

is not satisfactory as a transmitter p 
or sending apparatus. The transmitter commonly used is 
represented in cross-section in Fig. 311. In this figure, back 
of the mouthpiece, is a thin carbon disc, D. Back of this 




INDUCED CURRENTS 



351 



disc is a circular compartment containing granular carbon, 
g. The wires of the circuit are connected to the carbon 
disc and to the back of the case containing granular car- 
bon. The circuit through the transmitter also includes 
a voltaic or storage cell and the primary coil of an induc- 
tion coil. (See Fig. 312.) 

315. The action of the transmitter is explained as fol- 
lows : When the sound waves of the voice strike upon the 
carbon disc, the latter vibrates, alternately increasing and 
decreasing the pressure upon the granular carbon. When 
the pressure increases, the electrical resistance of the 





Transmitter 



Fig. 311. A telephone Fig. 312. Telephone instruments at one 
transmitter. end of a talking circuit. 

granular carbon is lessened, and when the pressure upon 
it is decreased, its resistance increases. This changing re- 
sistance causes fluctuations in the electric current that 
correspond exactly with the sound waves of the voice 
affecting it. 

316. A complete telephone system operating with a 
local battery is shown in Fig. 312. A person speaking 
into the transmitter causes a fluctuation in the electric 
current in the transmitter as described in Art. 315. This 
fluctuating current passes through the primary coil of 
the induction coil Ic. This fluctuating current produces a 
fluctuating magnetic field in its core. This fluctuating 
field induces an alternating current in the secondary coil 
which alternates just as the primary current fluctuates, 



352 PHYSICS , 

but with a much higher E.M.F. than the latter. The 
alternating current passes to the receiver which reproduces 
the speech as described in Art. 313. The line circuit in- 
cludes the secondary of the induction coil, the receiving 
instrument and the receiver of the sending instrument so 
that the voice is reproduced in both receivers. An elec- 
tric bell is placed at each station to call the attention of 
parties wanted. The movement of the receiver hook 
when the receiver is lifted, disconnects the bell and closes 
the talking circuit. The latter is opened and the bell 
connected when the receiver is hung up again. 

-Subscriber Une Central 



Fig. 313. Diagram of a- telephone system as used in a large exchange. 

In cities and towns, the telephone system in use differs 
from the one described in usually having one large bat- 
tery placed in the central exchange, instead of dry cells at 
each instrument. (See Fig. 313.) Also the operator at 
central is called by simply taking the receiver from the 
hook instead of being "rung up" by the subscriber. The 
operations of the transmitter, induction coil and receiver, 
however, are the same in all telephones. 

Important Topics 

1. Receiver: parts, action. 

2. Transmitter: parts, action. 

3. Induction coil, bell, line wires, etc. 

4. Action of the whole device. 

Exercises 

State three important electrical laws or principles that are 
employed in the operation of the telephone. What is the ap- 
plication of each? 



sound 353 

2. Connect the binding posts of a telephone receiver with a sensitive 
galvanometer and press on the diaphragm of the receiver; a 
deflection of the galvanometer will be noticed. Release the 
diaphragm and a reflection in the opposite direction is seen. 
Explain. 

3. Is the current passing through the transmitter the one going to 
the receiver of the instrument? Explain. 

4. Does the receiver at the telephone used by a person repeat the 
speech of the person? Explain. 

5. How many 0.5 ampere lamps can be used with a 6 ampere fuse? 

6. Why is it necessary to have a rheostat connected in series with 
a stereopticon or moving picture machine while a rheostat is 
not used with arc lights out doors? 

7. How many candle power should a 60 watt carbon incandescent 
lamp give, if its efficiency is 3.4 watts per candle power? 

8. Three incandescent lamps having resistances of 100, 150, and 
240 ohms, respectively, are connected in parallel. What is 
their combined resistance? 

Review Outline : Induced Currents 

Induced currents; 3 laws, illustrations. 

Construction, action, and uses of magneto, dynamo, induction 
coil, transformer, motor, telephone. Mercury arc rectifier. 

Terms primary, secondary, for coils and currents, armature, com- 
mutator, slip ring, brush, rectifier, open core, series, shunt, and 
compound connections for dynamos. 



23 



CHAPTER XV 
SOUND 

(i) Sound and Wave Motion 

317. What is a Sound? This question has two answers, 
which may be illustrated as follows: Suppose that an 
alarm clock is set so that it will strike in one week and that 
it is placed upon a barren rock in the Pacific Ocean by 

sailors who immediately sail away. If 
when the tapper strikes the bell at the 
end of the week no ear is within a hundred 
/^\ miles, is any sound produced? The two 

view-points are now made evident, for 
some will answer "no" others "yes." 
Those answering "no" hold that sound is 
a sensation which would not be produced 
if no ear were at hand to be affected. 
Those answering "yes" understand, by 
the term sound, a mode of motion capable 
of affecting the auditory nerves, and that 
sound exists wherever such motions are 
Fig. 314. The present. This latter point of view is 
brathfg. called the physical and is the one we are 

to use in this study. 

318. Source of Sound. If we trace any sound to its 
source, it will be found to originate in a body in rapid 
motion usually in what is called a state of vibration. To 
illustrate, take a tuning fork, strike it to set it in vibra- 
tion and place its stem firmly against a thin piece of wood ; 
the sound will be strengthened materially by the vibra- 

354 





sound 355 

tion of the wood. If now the vibrating fork is placed with 
the tips of the prongs in water, the vibration is plainly 
shown by the spattering of the water (Fig. 314). When 
one speaks, the vibrating body is in the larynx at the top 
of the windpipe. Its vibration may be plainly felt by 
the hand placed upon the throat while speaking. 

319. Sound Media. Usually sounds reach the ear 
through the air. The air is then said to be a medium for 
sound. Other substances may serve as a sound medium, 
for if the head is under water and two 
stones, also under water, are struck to- 
gether a sharp sound is heard. Also if 
one end of a wooden rod is held at the ear 
and the other end of the rod is scratched 
by a pin, the sound is more plainly per- 
ceived through the wood than through Yopump 
the air. Think of some illustration from _ Fl - s i 5-~ 

Sound does not 

your own experience of a solid acting as a travel in a vac- 
medium for sound. If an electric bell is uum " 
placed in a bell jar- attached to an air pump, as in Fig. 
315, on exhausting the air the loudness of the sound is 
found to diminish, indicating that in a perfect vacuum no 
sound would be transmitted. This effect of a vacuum 
upon the transmission of sound is very different from its 
effect upon radiation of heat and light. Both heat and 
light are known to pass through a vacuum since both 
come to the earth from the sun through space that so far 
as we know contains no air or other matter. Sound 
differs from this in that it is always transmitted by some 
material body and cannot exist in a vacuum. 

320. Speed of Sound. Everyone has noticed that it 
takes time for sound to travel from one place to another. 
If we see a gun fired at a distance, the report is heard a 
few seconds after the smoke or flash 13 seen. The time 



356 PHYSICS 

elapsing between a flash of lightning and the thunder 
shows that sound takes time to move from one place to 
another. Careful experiments to determine the speed 
of sound have been made. One method measures accu- 
rately the time required for the sound of a gun to pass 
between two stations several miles apart. A gun or 
cannon is placed at each station. These are fired alter- 
nately, first the one at one station and then the one at the 
other so as to avoid an error in computation due to the 
motion of wind. This mode of determining the speed 
of sound is not accurate. Other methods, more refined 
than the one just described have given accurate values for 
the speed of sound. The results of a number of experi- 
ments show that at the freezing temperature, oC, the 
speed of sound in air is 332 meters or 1090 ft. a second. 
The speed of sound in air is affected by the temperature, 
increasing 2 ft. or 0.6 meter per second for each degree 
that the temperature rises above oC. The speed decreases 
the same amount for each degree C. that the air is cooled 
below the freezing point. The speed of sound in various 
substances has been carefully determined. It is greater 
in most of them than in air. In water the speed is about 
1400 meters a second; in wood, while its speed varies with 
different kinds, it averages about 4000 meters a second; 
in brass the speed is about 3500 meters; while in iron it is 
about 5100 meters a second. 

321. The Nature of Sound.--We have observed that 
sound originates at a vibrating body, that it requires a 
medium in order to be transmitted from one place to an- 
other, and that it travels at a definite speed in a given sub- 
stance. Nothing has been said, however, of the mode of 
transmission, or of the nature of sound. Sounds continue 
to come from an alarm clock even though it is placed under 
a bell jar. ' It is certain that nothing material can pass 



sound 357 

through the glass of the jar. If, however, we consider 
that sound is transmitted by waves through substances the 
whole matter can be given a simple explanation. In order 
to better understand the nature of sound a study of waves 
and wave motion will be taken up in the next section. 

Important Topics 

Sound: two definitions, source, medium, speed, nature. 

Exercises 

1. Give two illustrations from outside the laboratory of the fact 
that sound is transmitted by other materials than air. 

2. Name the vibrating part that is the source of the sound in three 
different musical instruments. 

3. Is sound transmitted more strongly in solids, liquids or gases? 
How do you explain this? - 

4. How far away is a steamboat if the sound of its whistle is heard 
10 seconds after the steam is seen, the temperature being 2oC? 
Compute in feet and in meters. 

5. How many miles away is lightning if the thunder is heard 12 
seconds after the flash in seen, the temperature being 2SC? 

6. Four seconds after a flash of lightning is seen the thunder clap 
is heard. The temperature is qoF. How far away was the 
discharge? 

7. The report of a gun is heard 3 seconds after the puff of smoke 
is seen. How far away is the gun if the temperature is 2oC? 

8. An explosion takes place 10 miles away. How., long will it 
take the sound to reach you, the temperature being 8oF?. 
How long at oF.? 

9. How long after a whistle is sounded will it be heard if the dis- 
tance away is 34 mile, the temperature being qoF.? 

10. The report of an explosion of dynamite is heard 2 minutes 
after the puff of smoke is seen. How far away is the explosion 
the temperature being 77F.? 

(2) Waves 1 and Wave Motion 
322. Visible Waves. It is best to begin the study of 
wave motion by considering some waves which are familiar 

1 A wave is a disturbance in a substance or medium that is transmitted 
through it. 




358 physics 

to most persons. Take for example the waves that move 
over the surface of water (Fig. 316). These have an 
onward motion, yet boards or chips upon the surface 
simply rise and fall as the waves pass them. They are 
not carried onward by the waves. The water surface 
simply rises and falls as the waves pass by. Consider also 
the waves that may be seen to move across a field of tall 
/ x t| n grass or grain. Such waves are 

produced by the bending and 

rising of the stalks as the wind 

Fig. 316. Water waves. . A 

passes over them. Again, waves 

may be produced in a rope fastened at one end, by 
suddenly moving the other end up and down. These 
waves move to the end of the rope where they are 
reflected and return. The three types of waves just men- 
tioned are illustrations of transverse waves, the ideal case 
being that in which the particles move at right angles to 
the path or course of the wave. Such waves are there- 
fore called transverse waves. 

323. Longitudinal Waves. Another kind of wave is 
found in bodies that are elastic and compressible and have 
inertia, such as gases and 
coiled wire springs. Such 
waves may be studied by FlG . 3I7 ._ T he compression wave 

Considering a wire spring travels through the spring. 

as the medium through which the waves pass. (See 
Fig. 318.) 

If the end of the wire spring shown in Fig. 3 1 7 is struck 
the first few turns of the spring will be compressed. Since 
the spring possesses elasticity, the turns will move forward 
a little and compress those ahead, these will press the 
next in turn and so on. Thus a compression wave will 
move to the end of the spring, where it will be reflected 
and return. Consider the turns of the spring as they 



SOUND 



359 



move toward the end. On account of their inertia they 
will continue moving until they have separated from 
each other more than at first, before returning to their 
usual position. This condition of a greater separation of 
the turns of the spring than usual is called a rarefaction. 
It moves along the spring following the wave of compres- 
sion. The condensation and rarefaction are considered 
as together forming a complete wave. Since the turns 
of wire move back and forth in a direction parallel to that 
in which the wave is traveling, these waves are called 
longitudinal. 



\f\rmmmmmmm 

i 




Fig. 318. Longitudinal waves (1) in a spring, (2) in air, and (3) graphic 
representation showing wave length, condensations, and rarefactions. 

324. The transmission of a sound by the air may be 

understood by comparing it with the process by which a 
wave is transmitted by a wire spring. Consider a light 
spring (Fig. 318, 1) attached at the end of a vibrating 
tuning fork, K, and also to a diaphragm, D. Each 
vibration of the fork will first compress and then separate 
the coils of the spring. These impulses will be trans- 
mitted by the spring as described inArt. 315, and cause the 
diaphragm to vibrate at the same rate as the tuning fork. 
The diaphragm will then give out a sound similar to that 
of the tuning fork. Suppose that the spring is replaced 
by air, and the diaphragm, by the ear of a person, E, (Fig. 



360 PHYSICS 

318, 2.) When the prong of the fork moves toward the 
ear it starts a compression and when it moves back a 
rarefaction. The fork continues vibrating and these 
impulses move onward like those in the spring at a speed 
of about 1 1 20 ft. in a second. They strike the dia- 
phragm of the ear causing it to move back and forth or to 
vibrate at the same rate as the tuning fork, just as in the 
case of the diaphragm attached to the spring. 

325. Graphic Representation of Sound Waves. It is 
frequently desirable to represent sound waves graphically. 
The usual method is to use a curve like that in (Fig. 318, 3). 
This curve is considered as representing a train of waves 
moving in the same direction as those in Fig. 318 1 and 2, 
and also having the same length. The part of the wave 
A-B represents a condensation of the sound wave and the 
part B-C represents a rarefaction. A complete wave 
consisting of a condensation and a rarefaction is repre- 
sented by that portion of the curve A-C. The portion 
of the curve B-D also represents a full wave length as the 
latter is defined as the distance between two corresponding 
parts oj the adjacent waves. The curve, Fig. (318, 3) repre- 
sents not only the wave length, but also the height of the 
wave or the amount of movement of the particles along the 
wave. This is called the amplitude and is indicated by 
the distance A-b. Since the loudness or intensity of a 
sound is found to depend upon the amount of movement of 
the particles along the wave, the amplitude of the curve is 
used to indicate the loudness of the sound represented. 
All of the characteristics of a sound wave may be graphic- 
ally represented by curves. Such curves will be used 
frequently as an aid in explaining the phenomena of 
wave motion both in sound and in light. 

326. Reflections of Sound. It is found that a wave 
moving along a wire spring is reflected when it reaches the 



SOUND 



361 



end and returns along the spring. Similarly a sound wave 
in air is reflected upon striking the surface of a body. 
If the wave strikes perpendicularly it returns along the 
line from which it comes, if, however, it strikes at some 
other angle it does not return along the same line, but as in 
other cases of reflected motion, the direction of the re- 
flected wave is described by the Law of Reflected Motion 
as follows: The angle oj reflection is always equal to the 
angle of incidence. This law is illustrated in Fig. 319. 
Suppose that a series of waves coming from a source of 
sound move from H to 0. After striking the surface IJ 
the waves are reflected and move toward L along the 




Fig. 319. Law ot reflection. 




Fig. 320. An ear trumpet. 



line OL. Let PO be perpendicular to the surface // at O. 
Then HOP is the angle of incidence and LOP is the angle 
of reflection. By the law of reflected motion these angles 
are equal. In an ordinary room when a person speaks 
the sound waves reflected from the smooth walls reinforce 
the sound waves moving directly to the hearers. It is 
for this reason that it is usually easier to speak in a room 
than in the open air. Other illustrations of the reinforce- 
ment of sound by reflection are often seen. Thus an 
ear trumpet (Fig. 320), uses the principle of reflection 
and concentration of sound. So-called sounding boards 
are sometimes placed back of speakers in large halls to 
reflect sound waves to the audience. 



362 PHYSICS 

327. Echoes. An echo is the repetition of a sound 
caused by its reflection from some distant surface such as 
that of a building, cliff, clouds, trees, etc. The interval of 
time between the production of a sound and the perception 
of its echo is the time that the sound takes to travel from 
its source to the reflecting body and back to the listener. 
Experiments have shown that the sensation of a sound 
persists about one-tenth of a second. Since the velocity 
of sound at 2oC. is about 1130 ft., during one-tenth of a 
second the sound wave will travel some 113 ft. If the 
reflecting surface is about 56 ft. distant a short sound will 
be followed immediately by its echo as it is heard one- 
tenth of a second after the original sound. The reflected 
sound tends to strengthen the original one if the reflecting 
surface is less than 56 ft. away. If the distance of the 
reflecting surface is much more than 56 ft. however, the 
reflected sound does not blend with the original one but 
forms a distinct echo. The echoes in large halls especially 
those with large smooth walls may very seriously affect 
the clear perception of the sound. Such rooms are said 
to have poor acoustic properties. Furniture, drapery, 
and carpets help to deaden the echo because of diffused 
reflection. The Mormon Tabernacle at Salt Lake City, 
Utah, is a fine example of a building in which the reflect- 
ing surfaces of the walls and ceiling are of such shape and 
material that its acoustic properties are remarkable, a pin 
dropped at one end being plainly heard at the other end 
about 200 ft. away. 

Important Topics 

1. Waves: transverse, longitudinal; wave length, condensation, 
rarefaction. 

2. Wave motion: in coiled spring, in air, on water. 

3. Reflection of waves: law, echoes. 



SOUND 363 

Exercises 

1. A hunter hears an echo in 8 seconds after firing his gun. How 
far is the reflecting surface if the temperature is 2oC? 

2. How far is the reflecting surface of a bulding if the echo of 
one's footsteps returns in 1 second at ioC? 

3. Why is it easier to speak or sing in a room than out of doors? 

4. Draw a curve that represents wave motion. Make it exactly 
three full wave lengths, and state why your curve shows this 
length. Indicate the parts of the curve that correspond to a 
condensation and to a rarefaction. 

5. How long does it fake the sound of the "pin drop" to reach 
a person at the farther end of the building mentioned at the 
end of Art. 327? 

6. An echo is heard after 6 seconds. How far away is the reflect- 
ing surface, the temperature being 7oF. ? 

7. Why are outdoor band-stands generally made with the back 
curving over the band? 

8. A man near a forest calls to a friend. In 4 seconds the echo 
comes back. How far away is he from the forest? 

9. Would it be possible for us ever to hear a great explosion upon 
the moon? Explain. 

10. If a sunset gun was fired exactly at 6:00 p. M. at a fort, at what 
time was the report heard by a man 25 miles away, if the tem- 
perature was ioC? 

(3) Intensity and Pitch of Sounds 

328. Musical Sounds and Noises Distinguished. The 

question is sometimes raised, what is the difference 



Fig. 321. Graphic representations of (a) a noise, (b) a musical sound. 

between a noise and a musical sound? The latter 
has been found to be produced by an even and regular 




364 PHYSICS 

vibration such as that of a tuning fork or of a piano string. 
A noise on the other hand is characterized by sudden or 
irregular vibrations such as those produced by a wagon 
bumping over, a stony street. These differences may be 
represented graphically as in Fig. 321, (a) represents a 
noise, (b) a musical tone. 

329. Characteristics of Musical Sounds. Musical tones 
differ from one another in three ways or are said to have 
three characteristics, viz., intensity, pitch, and quality. 
Thus two sounds may differ only in intensity or loudness, 
that is, be alike in all other respects except this one, as when 
a string of a piano is struck at first gently, and again 

harder. The second 
sound is recognized as 
being louder. The dif- 

Fig. 322. Curve b represents a tone erence i s due to the 
of greater intensity. 

greater amplitude of vi- 
bration caused by more energy being used. Fig. 322 shows 
these differences graphically. Curve b represents the tone 
of greater intensity or loudness, since its amplitude of 
vibration is represented as being greater. 

330. Conditions Affecting the Intensity of Sound. 
The intensity of sounds is also affected by the area of the 
vibrating body. This is shown by setting a tuning fork 
in vibration. The area of the vibrating part being small, 
the sound is heard but a short distance from the fork. If, 
however, the stem of the vibrating fork is pressed against 
the panel of a door or the top of a box, the sound may be 
heard throughout a room. The stem of the fork has 
communicated its vibrations to the wood. The vibrating 
area, being greater, the sound is thereby much increased in 
intensity, producing a wave of greater amplitude. The 
same principle is employed in the sounding boards of 
musical instruments as in the piano, violin, etc. It is a 




SOUND . 365 

common observation that sounds decrease in loudness as 
the distance from the source increases. This is due to 
the increase of the surface of the spherical sound waves 
spreading in all directions from the source. Careful 
experiments have shown that in a uniform medium the 
intensity of a sound is inversely proportional to the square of 
the distance from its source. If a sound is confined so that 
it cannot spread, such as the sound moving through a 
speaking tube, it maintains its intensity for a considerable 
distance. An ear trumpet (see Fig. 320) also applies this 
principle. It is constructed so 
that sound from a given area 
is concentrated by reflection to 
a much smaller area with a 
corresponding increase in in 

., mi_ ui /t" Fig. 323. The megaphone, 

tensity. The megaphone (Fig. r 

323), and the speaking trumpet start the sound waves 
of the voice in one direction so that they are kept from 
spreading widely, consequently by its use the voice 
may be heard several times the usual distance. The in- 
tensity of a sound is also affected by the density of the 
transmitting medium. Thus a sound produced on a moun- 
tain top is fainter and thinner than one produced in a 
valley. The sound of a bell in the receiver of an air 
pump becomes weaker as the air is exhausted from the 
latter. Four factors thus influence the intensity of a 
sound, the area of the vibrating body, its amplitude of 
vibration, the distance of the source and the density of the 
transmitting medium. It is well to fix in mind the precise 
effect of each of these factors. 

331. Pitch. The most characteristic difference between 
musical sounds is that of pitch. Some sounds have a 
high pitch, such as those produced by many insects and 
birds. Others have a low pitch as the notes of a bass 



366 physics 

drum or the sound of thunder. How notes of different 
pitch are produced may be shown by the siren (Fig. 324). 
This is a disc mounted so as to be rotated on an axis. 
Several rows of holes are drilled in it in concentric circles. 
The number of holes in successive rows increases from 
within outward. If when the siren is rapidly rotated air 
is blown through a tube against a row of holes a clear 
musical tone is heard The tone is due to the succession 
of pulses in the air produced by the row of holes in the 
rotating disc alternately cutting off and permitting the 
air blast to pass through at very short intervals. If the 
blast is directed against a row of 
holes nearer the circumference the 
pitch is higher, if against a row 
nearer the center the pitch is 
lower. Or if the blast is sent 
against the same row of holes the 
pitch rises when the speed in- 
creases and lowers when the speed 

lessens. These facts indicate that 
Fig. 324. A siren. - . . 

the pitch of a tone is due to the 

number of pulses or vibrations that strike the ear each 

second; also that the greater the rate of vibration, the higher 

the pitch. 

332. The Major Scale. If a siren is made with eight 

rows of holes, it may indicate the relation between the 

notes of a major scale. To accomplish this, the number 

of holes in the successive rows should be 24, 27, 30, 32, 

36, 40, 45, 48. If a disc so constructed is rapidly rotated at 

a uniform rate, a blast of air sent against all of the rows 

in succession produces the tones of the scale These facts 

indicate that the relative vibration numbers of the notes 

of any major scale have the same relation as the numbers 

24, 27, 30, 32, 36, 40, 45, 48. 




SOUND 367 

The note called middle C is considered by physicists as 
having 256 vibrations a second. This would give the 
following actual vibration numbers to the remaining notes 
of the major scale that begins with "Middle C" D -288, 
E.-320, F.-341.3, G.-384, A.-426.6, B.-480, C.-512. 
Musicians, however, usually make use of a scale of slightly 
higher pitch. The international standard of pitch in this 
country and in Europe is that in which "A" has 435 vibra- 
tions per second. This corresponds to 261 vibrations 
for middle C. 

333. The Relation between Speed, Wave Length, and 
Number of Vibrations per Second. Since the notes from 
the various musical instruments of an orchestra are 
noticed to harmonize as well at a distance as at the place 
produced, it is evident that notes of all pitches travel at 
the same rate, or have the same speed. Notes of high 
pitch, having a high vibration rate produce more waves in a 
second than notes of low pitch, consequently the former 
are shorter than the latter. The following formula gives 
the relation between the speed (v), wave length (/), 
and number of vibrations per sec. (w) : 

v = / X n, or / = v/n 

that is, the speed of a sound wave is equal to the number 
of vibrations per second times the wave length, or the wave 
length is equal to the speed divided by the number of vibra- 
tions per second. This formula may also be employed to 
find the number of vibrations when the wave length and 
speed are given. 

Important Topics 

1. Difference between noise and music. 

2. Factors affecting intensity: area, amplitude, density, distance. 

3. Pitch, major scale, relative vibration numbers. 

4. Relation between speed, wave length and vibration rate. 



368 PHYSICS 

Exercises 

1. Give an illustration from your own experience of each of the 
factors affecting intensity. 

2. Write the relative vibration numbers of a major scale in which 
do has 120 vibrations. 

3. What is the wave length of the "A" of international concert 
pitch at 2 5C? Compute in feet and centimeters. 

4. At what temperature will sound waves in air in unison with 
"Middle C" be exactly 4 ft. long? 

5. Explain the use of a megaphone. 

6. What tone has waves 3 ft. long at 25C? 

7. What is the purpose of the "sounding board" of a piano? 

8. Two men are distant 1000 and 3000 ft. respectively from a 
fog horn. What is the relative intensity of the sounds heard by 
the two men? 

9. The speaking tone of the average man's voice has 160 vibra- 
tions per second. How long are the waves produced by him 
at 20C? 

(4) Musical Scales and Resonance 

334. A musical interval refers to the ratio between the 
pitches 1 of two notes as indicated by the results of the siren 
experiment. The simplest interval, or ratio between two 
notes is the octave, C':C, or 2:1 (48:24). Other important 
intervals with the corresponding ratios are the fifth, G:C, 
or 3:2 (36:24); the sixth, A:C, or 5:3 (40:24); the fourth, 
F:C, 4:3 (32:24); -the major third, E:C, or 5:4(30:24); and 
the minor third, G:E, 6:5. The interval between any two 
notes may be determined by finding the ratio between the 
vibration numbers of the two notes. Thus, if one note 
is produced by 600 vibrations a second and another by 400, 
the interval is 3:2, or a. fifth, and this would be recognized 
by a musician who heard the notes sounded together or 
one after the other. Below is a table of musical nomencla- 
tures, showing various relations between the notes of the 
major scale. 

1 Pitch as used here, means vibration rate. 



SOUND 
Table of Musical Nomenciatures 



369 



Name of note 


C 


D 


E 


F 


G 


A 


B 


C 


Frequency in terms of 
"do" 


n 


%n 


K 


%n 


H 


% 


!^ 


2M 




% 


10 A 


% 


% 


10 A 


% 


% 






Name of note in vocal 
music 


do 


re 


mi 


fa 


sol 


la 


ti 


do 


Treble clef. 











* 




1 


I 


y 
























A 



























<y 


fm 


1 
















& 






Vf 










a 










1/ 

Bass clef. 


^L 


a 













i> 


/itV 










& 












(rJ 






p* 


















1 , 


V>" 


ry 


pr 




















































1 














International pitch of 
treble clef 


261 

256 


293.6 

288 


326.3 

320 


348. 
341-3 


39i-5 
384 


435 
426.6 


489.4 


522 




Scientific scale 


480 


512 


Relative vibration num- 
bers. 


24 


27 


3 




3 


2 


36 


40 




45 


48 



335. Major and Minor Triads. The notes C, E, G (do, 
mi, sol) form what is called a major triad. The relative 
vibration numbers corresponding are 24, 30, 36. These in 
simplest terms have ratios of 4 :5 :6. Any three other tones 
with vibration ratios of 4:5:6 will also form a major triad. 
If the octave of the lower tone is added, the four make a 
major chord. Thus : F, A, C (fa, la, do) , 3 2 40 48, or 4 :5 :6, 
also form a major triad as do G, B, ~D'(sol, ti, re), 36 45 154, 
or 4:5:6. Inspection will show that these three major 
triads comprise all of the tones of the major scale D' 
being the octave of D. It is, therefore, said that the 
major scale is based, or built, upon these three major 
triads. The examples just given indicate the mathemat- 



21 



37 



PHYSICS 



ical basis for harmony in music. Three notes having 
vibration ratios of 10:12 :i 5 are called minor triads. These 
produce a less pleasing effect than those having ratios 
of 4:5:6. 

336. The Need for Sharps and Flats. We have consid- 
ered the key of C. This is represented upon the piano or 
organ by white keys only (Fig. 325). Now in order (a) 
to give variety to instrumental selections, and (b) to ac- 
commodate instruments to the range of the human voice, 
it has been necessary to introduce other notes in musical 
instruments. These are represented by the black keys 
upon the piano and organ and are known as sharps and 



I II III SI III II 

a I l/ill U I liUfjua 1 

Fig. 325. Section of a piano keyboard 



flats. To illustrate the necessity for these additional 
notes take the major scale starting with B. This will give 
vibration frequencies of 240, 270, 300, 320, 36, 400, 450, 
and 480. The only white keys that may be used with this 
scale are E 320 and B 480 vibrations. Since the second 
note on this scale requires 270 vibrations about halfway 
between C and D the black key C sharp is inserted. Other 
notes must be inserted between D and E (D sharp), 
between F and G (F sharp) , also G and A sharps. 

337. Tempered Scales. In musical instruments with 
fixed notes, such as the harp, organ, or piano, complications 
were early recognized when an attempt was made to adapt 
these instruments so that they could be played in all keys. 
For the vibration numbers that would give a perfect major 
scale starting at C are not the same as will give a perfect 



SOUND 371 

major scale beginning with any other key. In using the 
various notes as the keynote for a major scale, 72 different 
notes in the octave would be required. This would ake 
it more difficult for such instruments as the piano 
to be played. To avoid these complications as much as 
possible, it has been found necessary to abandon the simple 
ratios between successive notes and to substitute another 
ratio in order that the vibration ratio between any two 
successive notes will be equal in every case. The differ- 
ences between semitones are abolished so that; for example, 
C sharp and D flat become the same tone instead of two 
different tones. Such a scale is called a tempered scale. 
The tempered scale has 13 notes to the octave, wi h 12 
equal intervals, the ratio between two successive notes 
being the y\'2 or 1.059. That is, any vibration rate 

on the tempered scale may be computed by multiplying 
the vibration rate of the preceding note by 1.059 While 
this is a necessary arrangement, there is some loss in perfect 
harmony. It is for this reason that a quartette or chorus 
of voices singing without accompaniment is often more 
harmonious and satisfactory than when accompanied with 
an instrument of fixed notes as the piano, since the simple 
harmonious ratios may be employed when the voices are 
alone. The imperfection introduced by equal tempera- 
ment tuning is illustrated by the following table: 

CDE FGABC 

Perfect Scale of C . 2560 288.0 320.0 341.3 384.0 426.6 480.0 512.0 
Tempered Scale... 256.0 287.3 3 22 -5 34^-7 3&3-6 43- 5 4 8 3-3 5 I2 - 

338. Resonance. If two tuning forks of the same pitch 
are placed near each other, and one is set vibrating, the 
other will soon be found to be in vibration. This result 
is said to be due to sympathetic vibration, and is an example 
of resonance (Fig. 326). If water is poured into a glass 



372 



PHYSICS 



tube while a vibrating tuning fork is held over its top, 
when the air column has a certain length it will start 
vibrating, reinforcing strongly the sound of the tuning 
fork. (See Fig.327.) This is also an example of resonance. 
These and other similar facts indicate that sound waves 
started by a vibrating body will cause another 
body near it to start vibrating if the two have 
the same rate of vibration. Most persons 
will recall illustrations of this effect from 
their own experience. 



~ r 



Fig. 326. One tuning fork will 
vibrate in sympathy with the other, 
if they have exactly equal rates of 
vibration. 




Fig. 327. An air 

column of the proper 

length reinforces the 

sound of the tuning 
fork. 

339. Sympathetic vibration is explained as follows: 
Sound waves produce very slight motions in objects 
affected by them; if the vibration of a given body is exactly 
in time with the vibrations of a given sound each impulse 
of the sound wave will strike the body so as to increase 
the vibratory motion of the latter. This action continu- 
ing, the body soon acquires a motion sufficient to produce 
audible waves. A good illustration of sympathetic vibra- 
tion is furnished by the bell ringer, who times his pulls 
upon the bell rope with the vibration rate of the swing of 
the bell. In the case of the resonant air column over 
which is held a vibrating tuning fork (see Fig. 328), 
when the prong of the fork starts downward from 1 to 
2, a condensation wave moves down to the water surface 
and back just in time to join the condensation wave above 
the fork as the prong begins to move from 2 to 1; also 



SOUND 



373 



when the prong starts upward from 2 to 1, the rarefaction, 
produced under it moves to the bottom of the air column 
and back so as to join the rarefaction above the fork as the 
prong returns. While the prong is making a single 
movement, up or down, it is plain that the air wave moves 
twice the length of the open tube. During a complete 
vibration of the fork, therefore, the sound wave moves 
four times the length of the air column. In free air, the 
sound progresses a wave length during a complete vibra- 
tion, hence the resonant air column 
is one-fourth the length of the sound 
wave to which it responds. Experi- 
ments with tubes oi different lengths 
show that the diameter of the air 
column has some effect. upon the 
length giving best resonance. 
About 25 per cent, of the diameter 
of the tube must be added to the 
length of the air column to make 
it just one-fourth the wave length. 
The sound heard in seashells and 
in other hollow bodies is due to resonance. Vibrations 
in the air too feeble to affect the ear are intensified by 
sympathetic vibration until they can be heard. A tuning 
fork is of terl mounted upon a box called a resonator, which 
contains an air column of such dimensions that it rein- 
forces the sound of the fork sympathetic vibration. 




Fig 



328. Explanation of 
resonance. 



Important Topics 



1. Musical intervals: octave, sixth, fifth, fourth, third. 

2. Major chord, 4:5:6. 

3. Use of sharps and flats. Tempered scale. 

4. Resonance, sympathetic vibration, explanation, examples. 



374 physics 



Exercises 



1. What is a major scale? Why is a major scale said to be built 
upon three triads? 

2. Why are sharps and flats necessary in music? 

3. What is the tempered scale and why is it used? What instru- 
ments need not use it? Why? 

4. Mention two examples of resonance or sympathetic vibration 
from your own experience out of school. 

5. An air column 2 ft. long closed at one end is resonant to what 
wave length? What number of vibrations will this sound have 
per second at 25C? 

6. At 24C. what length of air column closed at one end will be 
resonant to a sound having 27 vibrations a second? 

7. A given note has 300 vibrations a second. What will be the 
number of vibrations of its (a) octave, (b) fifth x (c) sixth, (d) 
major third? 

8. In the violin or guitar what takes the place of the sounding 
board of the piano? , 

9. Can you explain why the pitch of the bell on a locomotive rises 
as you rapidly approach it and falls as you recede from it? 

10. Do notes of high or low pitch travel faster? Explain. 

11. An "A" tuning fork on the "international" scale makes 435 
vibrations per second. What is the length of the sound waves 
produced? 

(5) Wave Interference, Beats, Vibration of Strings 

340. Interference of "Waves. The possibility of two 
trains of waves combining so as to produce a reduced motion 
or a complete destruction of motion may be shown graphic- 
ally. Suppose two trains of waves of equal wave length 
and amplitude as in Fig. 329 meet in opposite phases. That 
is, the parts corresponding to the crests of A coincide with 
the 'troughs of B, also the troughs of A with the crests 
of B; when this condition obtains, the result is that shown 
at C, the union of the two waves resulting in complete 
destruction of motion. The more or less complete destruc- 



SOUND 



375 



Hon of one train of waves by another similar train is an 
illustration of interference. If two sets of water waves 
so unite as to entirely destroy each other the result is a 
level water surface. If twO trains of sound waves com- 
bine they may so interfere that silence results The con- 
ditions for securing interference of sound waves may 




Fig. 329. Interference of sound waves. 

readily be secured by using a tuning fork and a resonating 
air column. If the tuning fork is set vibrating and placed 
over the open end of the resonating air column (see Fig. 
328), an increase in the sound through resonance may be 
heard. If the fork is rotated about its axis, in some posi- 
tions no sound is heard While in other positions the sound 



1*2%3 



Fig. 330. At 2 is a con- 
densation; at 1 and 3 are rare- 
factions. 




Fig. 331. The condensations 
and rarefactions meet along the 
dotted lines producing silence. 



is strongly reinforced. Similar effects may be perceived 
by holding a vibrating fork near the ear and slowly rotat- 
ing as before. In some positions interference results 
while in other positions the sound is plainly heard. The 
explanation of interference may be made clear by the 
use of a diagram. (See Fig. 330.) Let us imagine that 



376 physics 

we are looking at the two square ends of a tuning fork. 
When the fork is vibrating the two prongs approach 
each other and then recede. As they approach, a 
condensation is produced at 2 and rarefactions at 1 
and 3. As they separate, a rarefaction is produced at 2 
and condensations at 1 and 3. Now along the lines at 
which the simultaneously produced rarefactions and con- 
densations meet there is more or less complete interference. 
(See Fig. 331.) These positions have been indicated by 
dotted lines extending through the ends of the prongs. 
As indicated above, these positions may be easily found 
by rotating a vibrating fork over a resonant air column, 
or near the ear. 

341. Beats. If two tuning forks of slightly different 
pitch are set vibrating and placed over resonating air 

B e 




1 ~ V \J \Ji 

J \J \J R 

Fig. 332. Diagram illustrating the formations of beats. 

columns or with the stem of each fork upon a sounding 
board, so that the sounds may be intensified, a peculiar 
pulsation of the sound may be noticed. This phenomenon 
is known as beats. Its production may be easily under- 
stood by considering a diagram (Fig. 332). Let the curve 
A represent the sound wave sent out by one tuning fork 
and B, that sent out by the other. C represents the effect 
produced by the combination of these waves. At R the 
two sound waves meet in the same phase and reinforce 
each other. This results in a louder sound than either 
produces alone. Now since the sounds are of slightly 



sound 377 

different pitch, one fork sends out a few more vibrations 
per second than the other. The waves from the first 
fork are therefore a little shorter than those from the other. 
Consequently, although the two waves are at one time in 
the same phase, they must soon be in opposite phases as at 
/. Here interference occurs, and silence results. Imme- 
diately the waves reinforce, producing a louder sound and 
so on alternately. The resulting rise and fall of the sound 
are known as beats. The number of beats per second 
must, of course, be the same as the difference between the 
numbers of vibrations per second of the two sounds. One 
effect of beats is discord. This is especially noticeable 
when the number of beats per second is between 30 and 
1 20. Strike the two lowest notes on a piano at the same 
time. The beats are very noticeable. 

342. Three Classes of Musical Instruments. There 
are three classes or groups of musical instruments, if 





Fig. 333. Turkish Fig. 334. The cornet, 

cymbals. 

we consider the vibrating body that produces the sound 
in each: (A) Those in which the sound is produced by a 
vibrating plate or membrane, as the drum, cymbals (Fig. 
333), e tc; (B) those with vibrating air columns, as the 
flute, pipe organ, and cornet (Fig. 334), and (C) with 
vibrating wires or strings, as the piano, violin, and guitar. 
It is worth while to consider some of these carefully. 



378 physics 

We will begin with a consideration of vibrating wires 
and strings, these often producing tones of rich quality. 

Let us consider the strings of a piano. (If possible, look 
at the strings in some instrument.) The range of the 
piano is 7^ octaves. Its lowest note, A 4 , has about 27 
vibrations per second. Its highest, C 4 , about 4176. 
This great range in vibration rate is secured by varying 
the length, the tension, and the diameter of the strings. 

343. The Laws of Vibrating Strings. The relations 
between the vibration rate, the length, the tension and the 
diameter of vibrating strings have been carefully studied 
with an instrument called a sonometer (Fig. 335). By 




Fig. 335. A sonometer. 

this device it is found that the pitch of a vibrating string 
is raised one octave when its vibrating length is reduced 
to one-half. By determining the vibration rate of many 
lengths, the following law has been derived: 
(Law I) The rate oj vibration oj a string is inversely pro- 
portional to its length. 

Careful tests upon the change of vibration rate produced 
by a change of tension or pull upon the strings show that 
if the pull is increased four times its vibrations rate is 
doubled, and if it is increased nine times its rate is tripled, 
that is: (Law II) The vibration rates of strings are directly 
proportional to the square roots of their tensions. 

Tests of the effects of diameter are made by taking wires 
of equal length and tension and of the same material but 
of different diameter. Suppose one is twice as thick as 



sound 379 

the other. This string has a tone an octave lower or vi- 
brates one-half as fast as the first. Therefore: 
(Law III) The vibration rates of strings are inversely pro- 
portional to Lie diameters. These laws may be expressed 

by a formula n <* 

The vibration of a string is rarely a simple matter. It 
usually vibrates in parts at the same time that it is vibrat- 
ing as a whole. The tone produced by a string vibrating 
as a whole is called its fundamental. The vibrating parts 
of a string are called loops or segments (see Fig. 336), while 
the points of least or no vibration are nodes. Segments 
are often called antinodes. 

344. Overtones. The quality of the tone produced by a 
vibrating string is affected by its vibration in parts when 



Fig. 336. A string yielding its fundamental and its first overtone. 

it is also vibrating as a whole. (See Fig. 336.) The tones 
produced by the vibration in parts are called overtones or 
partial tones. The presence of these overtones may 
often be detected by the sympathetic vibration of other 
wires near-by. What is called the first overtone is pro- 
duced by a string vibrating in two parts, the second over- 
tone by a string vibrating in three parts, the third overtone 
by its vibration in four parts and so on. In any over- 
tone, the number of the parts or vibrating segments of 
the string is one more than the number of the overtone. 
For example, gently press down the key of middle C of a 
piano. This will leave the string free to vibrate. Now 
strongly strike the C an octave lower and then remove 
the finger from this key. The middle C string will be 



380 PHYSICS 

heard giving its tone. In like manner try E 1 and G 1 , with 
C. This experiment shows that the sound of the C string 
contains these tones as overtones. It also illustrates 
sympathetic vibration. 

Important Topics 

1. Interference, beats, production, effects. 

2. Vibration of strings, three laws. 

3. Three classes of musical instruments. 

4. Fundamental and overtones, nodes, segments, how. produced? 
Results. 

Exercises 

1. What different means are employed to produce variation of 
the pitch of piano strings? For violin strings? 

2. How many beats per second will be produced by two tuning 
forks having 512 and 509 vibrations per second respectively? 

3. A wire 180 cm. long produces middle C. Show by a diagram, 
using numbers, where a bridge would have to be placed to cause 
the string to emit each tone of the major scale. 

4. How can a violinist play a tune on a single string? 

5. What are the frequencies of the first 5 overtones of a string 
whose fundamental gives 256 vibrations per second? 

6. One person takes 112 steps a minute and another 116. How 
many times a minute will the two walkers be in step? How 
many times a minute will one be advancing the left foot just 
when the other advances the right? 

7. Why is it necessary to have a standard pitch? 

8. How can the pitch of the sounds given by a phonograph be 
lowered? 

9. How many beats per second will occur when two tuning forks 
having frequencies of 512 and 515 respectively, are sounded 
together? 

10. Which wires of a piano give the highest pitch? Why? 

(6) Tone Quality, Vibrating Air Columns, Plates 

345. Quality. The reason for the differences in tone 
quality between notes of the same pitch and intensity as 



SOUND 



38l 



produced, e.g., by a violin and a piano, was long a matter of 
conjecture. Helmholtz, a German physicist (see p. 397) 
first definitely proved that tone quality is due to the vari- 
ous overtones present along with the fundamental and their 
relative intensities. If a tuning fork is first set vibrating by 
drawing a bow across it and then 
by striking it with a hard object, 
a difference in the quality of the 
tones produced is noticeable. It 
is thus evident that the manner 
of setting a body in vibration 
affects the overtones produced 
and thus the quality. Piano 
strings are struck by felt ham- 
mers at a point about one- 
seventh of the length of the 
string from one end. This point 
has been selected by experiment, 
it having been found to yield the 
best combination of overtones as shown by the quality 
of the tone resulting. 

346. Chladni's Plate. The fact that vibrating bodies 
are capable of many modes of vibration is well illustrated 




Fig. 337. Chladni's plate. 




F FB F B 

Fig. 338 Chladni's figures. 



by what is known as Chladni's plate. This consists of a 
circular or square sheet of brass attached to a stand at its 
center so as to be held horizontally. (See Fig. 337.) Fine 
sand is sprinkled over its surface and the disc is set vibrat- 



3 82 



PHYSICS 



ing by drawing a violin bow across its edge. The mode of 
vibration of the disc is indicated by the sand accumulat- 
ing along the lines of least vibration, called nodal lines. 
A variety of nodal lines each accompanied by its char- 
acteristic tone may be obtained by changing the posi- 
tion of the bow and by touching the fingers at different 
points at the edge of the disc. They are known as 
Chladni's figures. (See Fig. 338.) 

347. Manometric Flames. The actual presence of 
overtones along with the fundamental may be made visible 




Fig. 339. Manometric flame apparatus. 

by the manometric flame apparatus. This consists of a 
wooden box, C, mounted upon a stand. (See Fig. 339.) 
The box is divided vertically by a flexible partition or 
diaphragm. Two outlets are provided on one side of 
the partition, one, C, leads to a gas pipe, the other is a 
glass tube, D. On the other side of the partition a tube, 
E, leads to a mouthpiece. A mirror, M, is mounted so 
as to be rotated upon a vertical axis in front of F and near 
it. Gas is now turned on and lighted at F. The sound 
of the voice produced at the mouthpiece sends sound 
waves through the tube and against the diaphragm which 
vibrates back and forth as the sound waves strike it. 



SOUND 



3&3 



This action affects the flame which rises and falls. If 
now the mirror is rotated, the image of the flame seen in 
the mirror rises and falls, showing not only the funda- 
mental or principal vibrations but also the overtones. If 
the different vowel sounds are uttered in succession in the 
mouthpiece, each is found to be accompanied by its 
characteristic wave form (Fig. 340) . In some, the funda- 
mental is strongly prominent, 
while in others, the overtones 
produce marked modifications. 
Other devices have been invented 
which make possible the accurate 
analysis of sounds into their com- 
ponent vibrations, whilestill 
others unite simple tones to pro- 
duce any complex tone desired. 

348. The Phonograph. The 
graphophone or phonograph pro- 
vides a mechanism for cutting 
upon a disc or cylinder a groove 
that reproduces, in the varying 
form or depth of the tracing, 
every peculiarity of the sound waves affecting it. The 
reproducer consists of a sensitive diaphragm to which is 
attached a needle. The disc or cylinder is rotated under 
the reproducing needle. The irregularities of the bottom 
of the tracing cause corresponding movements of the 
needle and the attached diaphragm, which start waves 
that reproduce the sounds that previously affected the 
recorder. The construction of the phonograph has reached 
such perfection that very accurate reproduction of a great 
variety of sounds is secured. 

349. Wind Instruments. In many musical instruments 
as the cornet, pipe-organ, flute, etc., and also in whistles, 




Fig. 340. Characteristic 
forms of manometric flames. 



384 



PHYSICS 



the vibrating body that serves as a source of sound is a 
column of air, usually enclosed in a tube. Unlike vibrating 
strings, this vibrating source of sound changes but little 
in tension or density, hence changes in the pitch of air 
columns is secured by changing their length. The law 
being similar to that with strings, the vibration rates of 
air columns are inversely proportional to their lengths. 

If an open organ pipe be sounded by blowing gently 
through it, a tone of definite pitch is heard. Now if one 
end is closed, on being sounded again the pitch is found 



D 



C 

V 



m 




Fig. 341. (R) Cross-section of an organ pipe showing action of tongue 
at C. (a) The fundamental tone in a closed pipe has a wave length four 
times the length of the pipe; (b) and (c) how the first and second overtones 
are formed in a closed pipe; (d) the fundamental tone of an open pipe 
has a wave length equal to twice the length of the pipe; (e) and (/) first 
and second overtones of open pipe. 

to be an octave lower. Therefore, the pitch of a closed pipe 
is an octave lower than that of an open one of the same length. 
350. Nodes in Organ Pipes. Fig. 341, R represents a 
cross-section of a wooden organ pipe. Air is blown through 
A, and strikes against a thin tongue of wood C. This 



SOUND 385 

starts the jet of air vibrating thus setting the column of 
air in vibration so that the sound is kept up as long as air 
is blown through A. To understand the mode of vibra- 
tion of the air column a study of the curve that represents 
wave motion (Fig. 342) is helpful Let AB represent such 
a curve, in this 2, 4 and 6 represent nodes or points of 
least vibration, while 1, 3 and 
5 are antinodes or places of 
greatest motion. A full wave 
length extends from 15, or 
2-6. Now in the open organ FlG ' ^l^flllnl wl^S*^' 
pipe (Fig. 341^), the end of 

the air column d is a place of great vibration or is an anti- 
node. At the other end also occurs another place of 
great vibration or an antinode; between these two anti- 
nodes must be a place of least vibration or a node. The 
open air column therefore extends from antinode to anti- 
node (or from 1-3) or is one-half a wave length. The 
closed air column (Fig. 341a) extends from a place of great 
vibration at a to a place of no vibration at the closed end. 





Fig. 343. A clarinet. 

The distance from an antinode to a node is that from 1-2 
on the curve and is one-fourth a wave length. 

When a pipe is blown strongly it yields overtones. 
The bugle is a musical instrument in which notes of differ- 
ent pitch are produced by differences in blowing. (See 
Fig. 341 (d), (e), (/*). In playing the cornet different 
pitches are produced by differences in blowing, and by 
valves which change the length of the vibrating air column. 
(See Fig. 334.) The clarinet has a mouthpiece containing 



25 




386 PHYSICS 

a reed, similar to that made by cutting a tongue on a 
straw or quill. The length of the vibrating air column 
in the clarinet is changed by opening holes in the sides of 
the tube. (See Fig. 343.) 

351. How We Hear. Our hearing apparatus is ar- 
ranged in three parts. (See Fig. 344.) The external ear 
leads to the tympanum. The middle ear contains three 
bones that convey the vibrations 
of the tympanum to the internal 
ear. The latter is filled with a 
liquid which conveys the vibra- 
tions to a part having a coiled 
shell-like structure called the Coch- 
lea. Stretched across within the 
cochlea are some 3000 fibers or 

F Th strings. It is believed that each is 

sensitive to a particular vibration 
rate and that each is also attached to a nerve fiber. The 
sound waves of the air transmitted by the tympanum, the 
ear bones and the liquid of the internal ear start sympathetic 
vibrations in the strings of the cochlea which affect the 
auditory nerve and we hear. The highest tones percep- 
tible by the human ear are produced by from 24,000 to 
40,000 vibrations per second. The average person can- 
not hear sounds produced by more than about 28,000 vibra- 
tions. The usual range of hearing is about 11 octaves. 
The tones produced by higher vibrations than about 4100 
per second are shrill and displeasing. In music the range 
is 7^ octaves, the lowest tone being produced by 27.5 
vibrations, the highest by about 4100 per second. 

The tones produced by men are lower than those of 
women and boys. In men the vocal cords are about 18 
mm. long; in women they are 12 mm. long 
The compass of the human voice is about two octaves, 



SOUND 387 

although some noted singers have a range of two and one- 
half octaves. In ordinary conversation the wave length 
of sounds produced by a man's voice is from 8 to 12 ft. 
and that of a woman's voice is from 2 to 4 ft. 

Important Topics 
1. Tone quality. Fundamental and overtones. Chladni's plate. 
2 V Manometric flame apparatus. 

3. Phonograph recorder and reproducer. 

4. Air columns and wind instruments. 

5. How we hear. 

Exercises 

1. What determines the pitch of the note of a toy whistle? 

2. The lowest note of the organ has a wave length of about 64 ft. 
What is the length of a closed pipe giving this note? Of an 
open pipe? 

3. What is the first overtone of C? What are the second and third 
overtones? Give vibration numbers and pitch names or letters. 

4. Why is the music of a band just as harmonious at a distance of 
400 ft. as at 100 ft.? 

5. A resonant air column 60 cm. long closed at one end will respond 
to what rate of vibration at ioC? 

6. Can you find out how the valves on a cornet operate to change 
the pitch of the tone? 

7. How is the trombone operated to produce tones of different 
pitch? 

8. The lowest note on an organ has a wave length of about 64 ft. 
What must be the length of a closed pipe giving this note? 

g. What is the approximate length of an open organ pipe which 
sends out waves 4 ft. long? 

Review Outline: Sound 
Sound definition, source, medium, speed, nature. 
Waves longitudinal, transverse, illustrations. 
r , . . . f intensity area, amplitude, density, distance. 

_. . . q a . ] Prtch scales; major, tempered, tnads, N= 
[ V/L quality fundamental and overtones. 
Sympathetic Vibrations resonance, interference, beats, discord. 
Musical Instruments string, air column, membrane or plate. 
Laws of; (a) vibrating strings (3), (b) vibrating air columns (2). 



CHAPTER XVI 
LIGHT 

(i) Light, Its Rectilinear Propagation, Shadows 

352. A Comparison of Sound and Light. Light from 
the standpoint of physics is considered much as is sound, 
as a mode of motion; one affecting the ear, the other pro- 
ducing the result called vision. There are other differ- 
ences also worth considering, (a) "While sound travels 
as vibrations of some material medium, light .travels only 
as vibrations of the ether; solids, liquids, and gases act so 
as to hinder rather than to assist in its movement. That 
is, light travels best in a vacuum or in a space devoid of 
ordinary matter, (b) The speed of light is so great that 
at ordinary distances on the earth its motion is practically 
instantaneous. Experiments have shown that its speed 
is about 186,000 miles to 300,000 kilometers a second. 

353. Luminous and IUuminated Bodies. If we con- 
sider the objects within a room, some of them, as books and 
furniture, would be invisible if all light from external 
sources were excluded. On the other hand, some other 
objects, such as a lighted lamp, a burning coal, or a red 
hot iron,' would be seen if no outside light were pres- 
ent. Such bodies are said to be luminous. Most lumi- 
nous bodies are hot and become non-luminous on cooling. 
There are, however, some bodies that are luminous at 
ordinary room temperatures, as the firefly and some phos- 
phorescent paints. When light emitted by a luminous 
body strikes an object, a portion of it is always reflected. 

388 



LIGHT 



389 



It is this reflected light that makes the illuminated object 
visible. If the object is a sheet of glass, some of the light 
is transmitted. If a substance is so clear that objects can 
be seen through it, the substance is transparent, but if ob- 
jects cannot be seen through it, the substance is said to be 
translucent. Objects transmitting no light are opaque. 
Some of the light falling upon a body is neither reflected 
nor transmitted, but is absorbed and tends to warm 
the body. The light falling upon 
a body is therefore either reflected, 
transmitted, or absorbed. Thus Fig. 
345 represents light coming from 
S to a piece of glass GL. A por- 
tion of the light represented by R 
is reflected Another part A is 
absorbed and disappears, while 
stil another part T is transmitted 
and passes on. 

There is no sharply drawn line 
between transparent and opaque 
bodies. Very thin sheets of gold 
transmit a greenish light, and ex- 
periments have shown that sub- 
stances as transparent as clear 
water absorb enough light so that at considerable depths 
in an ocean or lake little or no light is ever found. All 
light whether from luminous bodies or reflected from non- 
luminous objects shows certain properties which will now 
be considered. 

354. The Rectilinear Propagation of Light. If a beam 
of light passes through a hole in a window shade into a 
darkened room, it is seen to follow a perfectly straight 
course. If a person while coughing holds a book before 
the face, the sound passes around the book and is heard 




Fig. 345. The light is 
transmitted (T), reflected 
(R), or absorbed (A). 



39 



PHYSICS 



at any point in the room while the face is hidden by the 
book. In other words, light ordinarily does not pass 
around corners as sound does, but travels in straight lines. 
This fact is made use of when one aims a gun or merely 
looks at an object. So well established in our minds is the 
idea that an object is in the direction from which we see the 
light coming to us from it, that we are sometimes deceived 
as to the real position of an object, when the course of the 
light from it has been changed by a mirror or some other 
reflecting surface. Many illusions are produced in this 
way, of which the mirage of the desert is one example. 
(See Art. 381.) 




Fig. 346. Shadow from a small source of light. 

355. Shadows. A shadow is the space from which light 
is cut of by an opaque body. Thus if a book (see Fig. 346) 
is held between a screen, N, and a small source of light, L, 




Fig. 347. Shadow when source of light is large. 

a shadow is produced which extends from the book to the 
screen Notice that the shadow is a space and not an 
area. If a large gas flame (see Fig. 347) is used as the 
source of light, the shadow of the book is no longer clear 



LIGHT 391 

cut at the edges as before, but has a darker central part 
with a lighter fringe of partial shadow at the edges. The 
dark portion within the shadow has all the light excluded 
from it and is called the umbra. The lighter portion of 
the shadow at the edges has only a part of the light from 
the flame cut off. This portion is called the penumbra. 
When one stands in sunlight his shadow extends from his 
body to the ground or object on which the shadow falls. 
At night we are in the earth's shadow, which extends out 
into space beyond the earth. 

356. Eclipses. Since the sun is a very large object the 
shadow cast by the earth contains both umbra and penum- 
bra. (See Fig. 348.) When the moon passes into the 




Fig. 348 Character of the earth's shadow. 

shadow of the earth, there is said to be an eclipse of the 
moon, while if the moon's shadow falls upon the earth, 
the portion of the earth cut off from the sun's light has 
an eclipse of the sun. 

357. Images by Small Apertures. The straight line 
movement of light makes possible the pin-hole camera, 
by which satisfactory photographs have been made. 
The action of this device may be illustrated by placing 
a luminous body, a lighted candle, an incandescent lamp, 
or a gas flame, in front of a piece of cardboard, S, which 
has a small opening in it Light from the object (see Fig. 
349) falls upon a screen, 5*2, so as to produce an inverted 
image. Other applications of this principle will be given 
later. 



392 



PHYSICS 



In Fig. 349 let PQ represent a gas flame, then light from point 
P at the top of the flame will pass in a straight line through the open- 
ing or aperture of the cardboard and strike at P2 at the bottom of 
the illuminated spot upon the screen. Light from Q passing in 
straight lines through the aperture will strike at Qz at the top of 
the lighted space. This spot of light will have the same outlines 
as the luminous body PQ and being formed as just described will 
be inverted. 




Fig. 349. Image formed by a small aperture is inverted. 

This spot of light, resembling in its outlines the flame, 
is called an image. An image is defined as an optical 
counterpart of an object. Images are formed in a variety 
of devices, such as apertures, mirrors, and lenses. The pin- 
hole camera is simply a light-tight box with a small aper- 
ture in one side Light passing through this aperture 
forms an image upon the opposite side of the interior of 
the box, of whatever object is in front of the camera. 
Light entering a room through a large aperture such as a 
window produces a multitude of overlapping images which 
blend to form a somewhat evenly illuminated surface. 



Important' Topics 



1. Light contrasted with sound (three differences). 

2. Bodies: transparent, translucent, opaque. 

3. Light: reflected, transmitted, absorbed. 



LIGHT . 393 

4. Light travels in straight lines, evidence, shadows, umbra, 
penumbra. 

5. Formation of images by small apertures. 

Exercises 

1. Consider the circumference of the earth as 25,000 miles. How 
many times would the speed of light cover this distance in a 
second? 

2. How soon after any great disturbance takes place on the sun, 
93,000,000 miles distant, can it be seen upon the earth? 

3. Construct a diagram of the moon's shadow. How much of the 
sun can one see when in the moon's umbra? When in its 
penumbra? Have you ever been in either? When? Have 
you ever been in the earth's umbra? In its penumbra? 

4. Explain, using a diagram, the formation of an inverted image by 
a small aperture. 

5. If the sun is 45 degrees above the horizon, what is the height 
of a pole casting a shadow 60 ft. long? 

6. If a shadow 6 ft. long is cast by a 10-ft. pole standing vertically 
upon a walk, how tall is the tree whose shadow is 42 ft. long, 
both measurements being made at the same time? 

7. Why are the shadows caused by an electric arc lamp so sharply 
defined? 

8. Why should schoolroom windows be all on one side and reach 
to the ceiling? 

9. What is the relation between the size of an image and its dis- 
tance from the aperture forming it? Can you prove this by 
geometry? 

10. What are silhouettes and how are they produced? 

(2) Photometry and the Law of Reflection 

358. Photometry. It is desirable at times to compare 
the intensities of illumination produced by light from 
different sources. This is done to determine the relative 
cost or effectiveness of various illuminants such as candles, 
kerosene and gas lamps, and electric lights The process 
of determining the relative intensity of lights or lamps is 
called photometry. (Photos = light.) 



394 



PHYSICS 



The unit for measuring the power of light is called a 
candle power. It is the light produced by a sperm candle 
burning 120 grains per hour. An ordinary gas light burns 
5 or more cubic feet of gas per hour and yields from 15 
to 25 candle power. A Welsbach gas lamp, consuming 
3 cu. ft. per hour, produces 50 to 100 candle power. 

Instead of using candles, for practical photometry, 
incandescent lamps standardized by the Bureau of Stand- 
ards are used for testing or calibration purposes. 

It is necessary to distinguish between the intensity of a 
luminous body, i.e., as a source of light, and the intensity 
of illumination upon some surface produced by a light. It 
is considered that two sources of light are of equal intensity 
if they produce equal illumination at equal distances. 

359. Law of Intensity of Light. A device for measuring 
the candle power of a light is called a photometer. Its use 
is based upon the law of intensity of light. The intensity of 
illumination of a surface is inversely proportional to the 
square of its distance from the source of light. This relation 
is similar to that existing between the intensity of a sound 
and the distance from its source. The following device 
illustrates the truth of this law in a simple manner. 




Fig. 350. The light spreads over four times the area at twice the 

distance. 

Cut a hole 1 in. square in a large sheet of cardboard (K) and place 
the card in an upright position 1 meter from an arc light or other 
point source of light (L). Now rule inch squares upon another card 
(M) and place it parallel to the first card and 2 meters from it. 
(See Fig. 350.) The light that passed through the hole of 1 sq. in. 



LIGHT 



395 



at a distance of i meter is spread over 4 sq. in. at a distance of 2 
meters. Therefore, the intensity of illumination on each square inch 
of M is one-fourth that upon the surface of K. If M is placed 3 
meters from the light, 9 sq. in. are illuminated, or the intensity is 
one-ninth that at 1 meter distance. 

These relations show that the intensity of illumination 
is inversely proportional to the square of the distance from 
the source of light. An application of the law of intensity 
is made in using a simple (Bunsen) photometer. This 
consists of a card containing a spot soaked with oil or 
melted wax. (See Fig. 351.) The lights whose intensities 




Fig. 351. The Bunsen photometer. 



are to be compared are placed upon opposite sides of the 
card. The card is then adjusted so that the spot appears 
the same on both sides. The illumination is now equal on 
both sides of the card and the candle powers of the two lights 
are proportional to the squares of their distances from the 
card. The simple device just described will give approxi- 
mate results only. For accurate results more elaborate 
apparatus is required. 

360. Measurement of the Intensity of Dlurnination. 
A standard candle (Art. 358) produces when lighted 1 
candle power. The illumination caused by this upon a 
surface 1 ft. away and at right angles to the light rays 



396 PHYSICS 

is called a foot-candle. It is the unit of intensity of 
illumination. A 4-candle-power lamp, at a distance of 
1 ft., produces 4 foot-candles. A 1 6-candle-power lamp 
at a distance of 2 ft. also produces 4 foot-candles-(i6 -f- 2 2 ). 
The intensity of illumination required for a good light 
for seeing varies with the conditions. Thus, for stage and 
store lighting about 4 foot-candles are needed, while homes 
and churches may require but 1 foot-candle. 

Too great an intensity of illumination is as harmful as 
not enough. Exposed lights having an intensity of more 
than 5 candle power per square inch are often a cause 
of eye trouble. Such lights should be protected by frosted 
globes. 

A pleasing form of lighting for large halls and public 
buildings is the indirect system. In this, the lamps are 
hidden by reflectors which, throw the light upon the ceiling 
from which it is diffused over the room. This form of 
lighting is more expensive than other systems since but 
a part of the light is reflected. Its cost therefore is an 
important factor when considering its use. 

361. The Reflection of Light. 
The light reflected from the surfaces 
of bodies about us gives us informa- 
tion concerning our surroundings. 
A knowledge of the behavior of 
light undergoing reflection is not 
usually gained from ordinary obser- 
vation. The law of reflection of light 

Fig. 352. B' is as far may be shown, however, by an ex- 
back of the mirror as B , 
is in front of it. penment. 

A plane mirror, M, is held in a vertical position resting upon a 
sheet of paper. (See Fig. 352.) Pins are set upright in the paper 
at A and B. On placing the eye along the line AC and looking 
toward the mirror an image of B may be seen in the mirror due to 




Christian Huygens (1629-1695). 
Dutch physicist; invented the pen- 
dulum clock (1656); developed the 
wave theory of light; discovered 
polarization of light (1690). 





Christian Huygens 
(Popular Science Monthly) 



Hermann von Helmholtz (1821- 
1894) Germany. Established the 
doctrine of conservation of energy; 
made many discoveries in sound; 
invented the ophthalmoscope; 
established the physical basis of 
tone quality. 



H. V. Helmholtz 
By Permission of the Berlin Photo- 
graphic Co., New York." 



LIGHT 399 

the light reflected from its surface. Pins C and D are now set in 
the paper so that when one looks along the line BD toward the 
mirror one may see all four pins apparently in one line. This 
indicates that the light from A and C passing along CA toward 
O is reflected back along the light CBD. By means of a ruler, 
draw lines through BD and A C till they intersect at 0. Also draw 
PO perpendicular to the mirror at 0. 

Then the angles AOP and BOP will be found equal. 
These are called the angles of incidence and reflection 
respectively. The law of reflection is therefore stated: 
The angle of reflection is equal to the angle of incidence. 
These angles are in the same plane, that of the paper. 
This law applies in all cases of reflection of light. It is 
similar to the law of reflection of sound (Art. 326.) 

Important Topics 

1. Photometry, law of intensity, candle power, foot-candle. 

2. Intensity of illumination. 

3. Reflected light and law of reflection. 

Exercises 

1. Both sides of a card are equally illuminated when two lights are 
on opposite sides of it and 10 and 30 cm. respectively from it. 
What are their relative intensities? 

2. What are the relative intensities of illumination from a gas light 
upon a book 6 ft. and 2 ft. respectively from the light? 

3. Which is more expensive per candle power? How many times 
as expensive? A 50- watt 16-can die-power incandescent lamp 
at 10 cents per kilowatt-hour or a 100-candle-power Welsbach 
light burning 5 cu. ft. of gas per hour at 80 cents per 1000 cu. ft. 
of gas. (Find cost of each per hour, and then the cost of 1 
candle power hour for each.) 

4. Why are not ordinary shadows perfectly dark? 

5. At what distance will a 16-candle-power lamp give the same 
illumination as 'single candle at 10 in.? 

6. If the sun is at an elevation of 30 degrees what is the angle of 
incidence at which it strikes the surface of water. What is the 
angle between the incident and the reflected rays? 



400 PHYSICS 

7. What is the difference between the phenomena of reflection of 
light from a white sheet of writing paper and from a piece of 
clear window glass? 

8. A horizontal ray of light, traveling due east, strikes a vertical 
mirror so that after reflection it is traveling due north. If the 
mirror be now turned 10 degrees about a vertical axis, the north 
edge moving east, what will be the direction of the reflected ray? 

9. The necessary illumination for reading is about 2 foot-candles. 
How far away may an 8-candle-power lamp be placed? 

10. What is the illumination in foot-candles upon a surface 20 ft. 
from an arc lamp having an intensity of 1000 candle power? 

11. How far from a 100-candle-power Welsbach light would the 
illumination be 2 foot-candles? 

(3) Mirrors and the Formation or Images 

362. Mirrors. The many purposes served by mirrors 
in our everyday life has made their use familiar to every- 
one. Yet without study and experiment few understand 




a b 

Fig. 353. Reflection of light, (a) diffused, (b) regular. 



their properties and action. Any smooth surface may 
serve as a mirror, as that of glass, water, polished wood, 
or metal. Most objects, unlike mirrors, have irregular 
surfaces; these scatter or diffuse the light that falls upon 
them. (See Fig: 353a.) This is called diffused or irregular 
reflection. The reflection of light from the smooth surface 
of a mirror is regular. (See Fig. 3536.) In every case of 
reflected light, however, the angle of reflection equals the 
angle of incidence, diffusion being due to the irregu- 



LIGHT 



401 



larity of the surface. It is by means of the light "diffused" 
from the surface of illuminated bodies, such as plants, 
animals, food, and manufactured articles, that we "see" 
the various objects about us, and it is this light that 
enables us to judge of their distance, size, form, color, etc. 
The moon is seen by the sunlight reflected from its surface. 
Moonlight is therefore sunlight diffused by reflection. 
The new moon is that phase or condition of the moon when 
only a narrow strip of the moon's illuminated surface 
is turned toward the earth. At the time of the full 
moon the whole illuminated surface is seen. 

363. Images Formed by a Plane Mirror. The most 
common use of mirrors is in the formation of images. The 
way in which images are formed 
by a plane mirror may be illus- 
trated by diagrams. Thus in 
Fig. 354, let L represent a 
luminous body and E and E' 
two positions of the observer's 
eye. Take any line or ray as 
LO along which the light from 
L strikes the mirror O-O' . It 
will be reflected so that angle 
LOP equals angle POL*. Sim- 
ilarly with any other ray, as 
LO', the reflected ray O'E' has 
a direction such as that angle L'O'E' equals angle P'O'E '. 
Any other rays will be reflected in a similar manner, 
each of the reflected rays appearing to the eye to come 
from a point V behind the mirror. 

364. Light Waves and Wave Diagrams. Just as a 
stick continually moved at the surface of a body of water 
sets up a series of waves spreading in all directions, so one 
may imagine a train of waves sent out by a luminous 



< 




Fig. 354. The virtual image 
of a fixed object as seen in a 
plane mirror, has the same 
location from every position of 
the observer's eye. 



402 



PHYSICS 



body L (as in Fig. 355) to the mirror MN. These waves 
will be reflected from the mirror as if the source of light 
were at L '. It is much simpler and more convenient to 
locate the position of the image of a point by the use of 
lines or "rays" (as in Fig. 354) than by "the wave diagram 
(as in Fig. 355) . In all ray diagrams, however, it should be 
kept in mind that the so-called ray is a symbol used to 
represent the direction taken by a part of a light wave. 




Fig. 355 Wave diagram of image formed in a plane mirror. 

Thus in Fig. 354, the light from L moving toward is 
reflected to E along the line OE, the heavy lines rep- 
senting rays. 

365. To locate the image of an object formed by a 
plane mirror requires simply an application of the law 
of reflection. Thus in Fig. 356 let AB represent an object 
and MN a plane mirror. Let A A' be a ray from A striking 
the mirror perpendicularly. It is therefore reflected back 
along the same line toward A . Let A O represent any other 
ray from A. It will be reflected along OE so that angle 
r equals i. The intersection of AC and OE at A' behind 
the mirror locates the image of the point A, as seen by 
reflection from the mirror. The triangles A CO and 
A' CO may be proved equal by geometry. Therefore 



LIGHT 



403 



A'C equals AC. This indicates that the image of a point 
formed by a plane mirror is the same distance back of the 
mirror as the point itself is in front of it. This principle 
may be used in locating the image of point B at B'. Locat- 
ing the position of the end points of an image determines 
the position of the whole image as A'B' . 




Fig. 356. The image A' B' is as far back of the mirror M N as the 
object A B is in front of the mirror. 



366. How the Image is Seen. Suppose the eye to be 
placed at E. It will receive light from A by reflection 
as if it came from A'. Similarly light starting from B 
reaches the eye from the direction of B' . There is nothing 
back of the mirror in reality that affects our sight, the light 
traveling only in the space in front of the mirror. Yet 
the action of the reflected light is such that it produces 
the same effect as if it came from behind the mirror. 
Images such as are seen in plane mirrors are called virtual 
to distinguish them from real images, in which light 
actually comes to the eye from the various parts of the 
visible image, as from the real image formed by a project- 
ing lantern upon a screen, or by an aperture as in the pin- 



44 



PHYSICS 



hole camera. Real images therefore are those that can 
be obtained upon a screen while virtual images cannot. 

367. Multiple Reflection. If the light from an object 
is reflected by two or more mirrors various effects may be 
produced, as may be illustrated by the kaleidoscope. This 
consists of three plane mirrors so arranged that a cross- 
section of the three forms an equilateral triangle. The 




Fig. 357. Perspective view 
of "Pepper's ghost." 



Fig. 358. Diagram of the "Pepper 
Ghost" illusion. 



mirrors are placed in a tube across the end of which is a 
compartment with a translucent cover containing pieces 
of colored glass. On. looking through the tube, the reflec- 
tions from the several surfaces produce beautiful hexago- 
nal designs. 

368. Optical Illusions by a Plane Mirror. The illusion 
called Pepper's Ghost is typical of many illusions produced 
by reflection. It may be illustrated by taking a piece of 
plate glass, M-N, a tumbler of water, W, and a lighted 
candle, C, placed in a box, B, having one side open and 
arranged as shown in perspective in Fig. 357, and in 
section in Fig. 358. If the effect is produced in a dark- 
ened room, the observer at E sees a virtual image of the 
lighted candle as if it were in the glass of water, the water 
being seen by transmitted light through the plate glass, the 




LIGHT 45 

latter forming a virtual image of the candle by refection. 
Some of the illusions produced by this means are: (a) 
the figure suspended in mid air; (b) the bust of a person 
without a trunk; (c) the stage ghost; (d) the disappearing 
bouquet. 

369. Concave Mirrors. Another useful piece of phys- 
ical apparatus is the 
concave spherical mir- 
ror. It is frequently 
made from plano-con- 
vex lenses by silvering 

the convex surface of Fig. 359. Action of a concave mirror on 
. . . parallel rays of light. 

the lens, thus making a 

concave reflecting surface from the inner surface of the 
silvered part; they are also made by polishing the inner 
surfaces of metallic spherical shells. The concave mirror 
is represented in section in Fig. 359 by the curve MN; 
C is the center of curvature or the center of the surface of 
which this mirror MN is a part; the line VC through the 

center V of the mirror is 
\ called the principal axis; 
while any other line pass- 
ing through C is called 
a secondary axis. The 
point midway between 
Fig. 360. Real image formed by a the vertex V and center 

concave mirror. r /^ 11 j 

of curvature G is called 
the principal focus, F. It is the point through which 
parallel incident rays pass after reflection. The angle 
MCN which the curve of the mirror subtends at the 
center is called the aperture of the mirror. We learned in 
Art. 361, the angle of reflection of a ray of light is always 
equal to the angle of incidence no" matter what the nature 
of the reflecting surface may be. If the reflecting surface 




406 PHYSICS 

is a regular concave surface, like the inner surface of a 
sphere, the rays of light coming from a point source may 
after reflection come to a focus, forming a real image. 
The two extreme points of an object should be selected" 
for locating its image; Fig. 360 shows the construction. 
The real images formed by concave mirrors are always 
inverted. The principal focus of a concave mirror may 
be observed by holding the mirror in a beam of sunlight 
entering a darkened room. The sun's rays after reflec- 
tion converge to form a small, round, intense spot of light, 
which is a real image of the sun, located at the principal 
focus of the mirror. The distance of the principal focus 
from the mirror is the least distance that a real image 
can be formed in front of a concave mirror. 

370. Virtual Images by Concave Mirrors. When light 
comes from a small point situated between a concave mir- 
ror and its principal focus, the 
reflected rays are divergent and 
hence no real image of the object 
can be found in front of the 
mirror. But if the rays are ex- 
tended behind the mirror they 
will meet in a point called the 
virtual focus. This is the point 

Fig. 361 . Virtual image f rom wn i cn they appear to come, 
formed by a concave mirror. , ... 

Any image of an object situated 
between the principal focus and a concave mirror is 
therefore a virtual image, erect and larger than the 
object. (See Fig. 361.) 

371. Construction of Real Images. There are five 
positions at which an object may be situated in front of a 
concave mirror, namely: (1) beyond C; (2) at C; (3) be- 
tween C and F; (4) at F and (5) between F and V. There 
are two ways by means of which the image formed at each 



LIGHT 407 

of these positions may be located, namely; (1) experi- 
mentally, by allowing the rays of light from a luminous 
body to focus on a screen and (2) diagrammatically. By 
the latter method the two rays of light are considered the 
course of each of which may easily be determined; first, the 
ray which strikes the mirror parallel to its principal axis 
and which after reflection passes through the principal 
focus; second, the ray which passing through the center 
of curvature strikes the mirror at right angles and there- 
fore after reflection must pass directly back along its 
incident path. Where these two reflected rays intersect 
is located the real image of the object. Whenever these 
two rays of light do actually intersect, as in Fig. 360, a 
real image (ab) is formed of the object AB. 

The points A and a, B and b and others similarly 
situated on an axis extending through the center of curva- 
ture C are called conjugate foci, for they are so related that 
an object being at either one, its image will be found at the 
other. 

372. The Convex Mirror. There are few practical 
.uses to which convex mirrors can be put. They are some- 
times used to give the chauff- 
eur of an automobile a view ~0^\/7 
of the road behind him. It is > -vl^ ^^ l>,-. 

then attached to the wind > < ~ZJ y~~X^ > 

shield by a short rod. The > ^^y^C 

reflected rays coming from *^N 

a convex mirror are always FlG . 3 6 2 .-Actiqn of a convex 

divergent (see Fig. 362), hence or u P on parallel rays of 

the image is always virtual and 

located behind the reflecting surface. The method of 

construction for images formed by a convex mirror is 

similar to that for concave mirrors. (See Fig. 363.) 

The center of curvature and principal focus are behind 



408 



PHYSICS 




Fig. 363. Construction of an 
image by a convex mirror. 



the mirror and consequently the reflected rays have to 

be produced backward until 
they meet. The images are 
always virtual, erect and smaller 
than the object. 

373. Spherical Aberration. 
Sometimes in a concave 
mirror when the aperture 
MCN (Fig. 364) is large the 
images are blurred or indis- 
tinct. This is due to the fact 
that the incident rays near the outer edge of the mirror 
do not focus after reflection at the same point as those 
which pass into the mirror near the vertex, but cross 
the principal axis at points 
between the mirror and 
principal focus as is shown 
in Fig. 364; this result is 
called spherical aberration. 
The larger the aperture of 
the mirror the more the 
image is blurred. Con- 
cave mirrors in practical 
use do not have an aper- 
ture much greater than 10 
degrees. This non-focus- 
ing of the rays of light by 
curved reflecting surfaces 
may be noticed in many 
places, as when light is 
reflected from the inside 
of a cup that contains 

milk or from the inside of a wide gold ring placed on top 
of a piece of white paper. The pupil will note other 









&M 


> 

) 






> 

) 


MS 


zA 


c 


&* 










T 




p 


> 




m 



N 

Fig. 364. Illustrations of Spherical 
Aberration. 



LIGHT 



409 



instances. This curve of light observed is called the 
caustic by reflection. 

374. Parabolic Mirrors. The best possible surface to 
give to concave mirrors is parabolic. This is a curve which 
may be generated by moving a point 
so that its distance from a fixed point 
and a fixed line are always equal. 
If a source of light is placed at F 
the rays after reflection are rendered 
parallel. See Fig. 365. This reflector 
is used in automobile lamps, head- 
lights of locomotives, search-lights, 
etc. It is also used in large reflecting 
astronomical telescopes to collect as 
large an amount of light as possible from distant stars 
and bring it to a focus. Such mirrors may be made 
exceedingly accurate. 




Fig. 



365 . Parabolic 
mirror. 



Important Topics 

1. Reflection: regular, diffused; plane mirrors; laws of reflection. 

2. Formation and location of images by plane mirrors. Wave and 
ray diagrams. 

3. Multiple reflection, illusions. 

4. Curved mirrors, uses; concave, convex, parabolic. 



Exercises 

1. Distinguish between regular and diffused reflection. By means 
of which do we see non-luminous bodies? 

2. Could a perfect reflecting surface be seen? Explain. 

3. A pencil is stood upright in front of a plane mirror set at an 
angle of 45 degrees to the vertical. Shown by a diagram the 
location and position of the image. 

4. Show by diagrams the position and location of the images of a 
pencil (a) when standing erect and in front of a vertical mirror, 
(b) When standing upon a horizontal mirror. 

5. What is the difference between a real and a virtual image? 



4IO PHYSICS 

6. A standard candle and a lamp give equal illuminations to a 
screen that is i ft. from the candle and 6 ft. from the lamp. 
What is the candle power of the lamp? Explain. 

7. Why are walls finished in rough plaster or painted with soft 
tones without gloss better for schoolrooms than glossy paints 
or smooth white plaster? 

8. Try to read a printed page by looking at its image in a mirror. 
Write your name backward on a sheet of paper, and then look 
at the image of the writing in a mirror. What effect is pro- 
duced by the mirror in each case? 

9. If the point of a pencil is held to the surface of a piece of plate- 
glass mirror two or more images may be seen in the mirror. 
Explain. 

10. Given a small lighted candle, a concave mirror, a meter stick, 
and a white screen, how would you prove the statements made 
in Arts. 369 and 370 concerning the location of images formed 
by concave mirrors? Make the diagram in each case. 

11. Why do images seen in a quiet pond of water appear inverted? 
Explain by a diagram. 

(4) Refraction of Light 

375. Common Examples of Refraction. Everyone has 
noticed the apparent bending of an oar, of a stick, or of a 
spoon when placed in water (see 
Fig. 366), while many have observed 
that the bottom of a pond or stream 
looks nearer to the surface than it 
really is. These and similar illusions 
are due to the refraction or bending 
Fig. 366. The stick of light rays as they pass from one 

appears to be bent on j. ,-, mi. 1 

account of refraction. medium to another. The principles 
of refraction are among the most use- 
ful found in the study of light since application is made of 
them in the construction and use of important optical 
instruments, such as the camera, microscope, telescope, 
and the eye. 




LIGHT 



411 



\ 







376. Action of Light Undergoing Refraction. If a 

beam of sunlight be admitted to a darkened room and re- 
flected by a mirror so that it strikes the surface of water 
in a glass jar, a part of the beam may be seen to be reflected 
while another portion is transmitted through the water 
(Fig. 367). The re- 
flected beam follows 
the law of reflection 
while the transmitted 
beam is seen to be 
refracted, or to have 
its courses slightly 
changed in direction 
upon entering the 
water. If the mirror 
is turned so that the 
angle at which the 

light Strikes the water Fig. 367. Part of the ray is reflected and 
1. j j.\. P art passes into the water and is refracted. 

is changed, the amount r " 

of refraction or change of course of the light is varied. 
When the light strikes the water perpendicularly there 
is no refraction. On the other hand, the greater the 

angle at which the light strikes 
the water the greater the 
bending. 

377. Laws of Refraction. 
The action of light on enter- 
ing, passing through, and 
leaving a great variety of 
substances has been care- 
fully studied. A summary of 
the results of these observations is given in the following 
laws of refraction: I. When light enters a transparent body, 
perpendicularly, it passes on without changing its direction. 




Fig. 368. Illustrating the laws 
of refraction of light. 



412 



PHYSICS 




II. When light enters a denser transparent body obliquely, it 
is bent toward the perpendicular; when light enters a less dense 
body obliquely, it is bent away from the perpendicular. 
(See Fig. 368.) 

378. The cause of refraction may be illustrated by 
considering a line of men moving across a field and occupy- 
ing at equal time intervals the 
successive positions I, 2, 3, etc., 
indicated in Fig. 369. Sup- 
pose that the upper and lower 
parts of the field have a smooth 
hard surface, while at the center 
is a strip of newly ploughed 
ground. The line -will move 
more slowly over the ploughed 
field than over the hard field. 
This will result in a retardation 
of the end of the line first strik- 
ing the soft ground with a 

resulting change of direction of the line, toward the 
perpendicular to the edge of the field {on entering the 
place of more difficult travel), and away from the per- 
pendicular on moving into a place where increased speed 
results. 

379. Index of Refraction. By studying the change of 
direction of the marching men as shown in Fig. 369 it is 
evident first that it is due to a difference in speed in the 
two media. It is not easy to measure the speed of light 
in a medium. However, the amount of refraction may be 
determined easily and from this the relative speed may be 
computed. The number that expresses the ratio of the speed 
of light in air to its speed in another medium is called the 
index of refraction of that medium. The relative speeds of 
light, or the indices of refraction for some substances, are: 



Fig. 369. Diagram illustrat- 
ing the cause of refraction. 



LIGHT 



413 



water, 1.33, crown glass, 1.5 1, flint glass, 1.6 1, diamond, 
2.47, carbon bisulphide, 1.64. 

380. Plates, Prisms, Lenses. The refraction of light 
is usually observed when it is passing through a plate, a 
prism, or a lens. The im- 
portant differences between 
the effects of each in refract- 
ing light are illustrated in 
Figs. 370, 371 and 372. In 
Fig. 370 it is seen that the 
refraction of the ray on enter- 
ing the glass is counteracted 
by the refraction away from 
the perpendicular upon leav- 
ing it. So that the entering 
and emergent rays are par- 
allel. In Fig. 371 the refraction at the two surfaces of 
the prism results in a change of direction of the ray, the 
course being bent toward the thicker part of the prism. In 




Fig. 370. The incident ray and 
the emergent ray are parallel. 




F 



Fig. 371. Effect of a prism upon Fig. 372. The convex lens brings 
a ray of light. the rays of light to a focus. 

Fig. 372 it may be noticed that the convex lens resembles 
two prisms with their bases together. Since all parts of 
the lens refract light toward the thicker part, the center, 
the effect of the convex lens is to bring the rays of light to 
a focus, at F. 

381. Total Reflection. It has been shown that when 
light passes from a denser to a lighter medium, as from glass 



414 



PHYSICS 



or water to air, that the beam is refracted away from the 
perpendicular. This is illustrated in Fig. 373. The 
diagram represents the change in the course of a ray of 
light that passes through water to a surface with air above 
it. A ray striking perpendicularly passes through with- 
out refraction. Other rays show increasing refraction 
with increasing angle of-incidence. For one ray the angle 
of refraction is so large that the refracted ray is parallel 
to the surface When this condition is reached, the 





Fig. 373. An example of total reflection. 



Fig. 374. Total reflection 
in a right-angle prism. 



angle of incidence is called the critical angle. Any increase 
in the angle of incidence causes all of the light to be re- 
flected as is the beam E. This action is called total 
reflection, the course of the reflected ray being according 
to the law of reflection. A right-angle prism (see Fig. 374) 
is often used where a mirror would ordinarily be employed, 
the total reflection occurring within the prism giving more 
satisfactory results than a mirror. See Art. 398 for a 
description of the Zeiss binocular field-glass for an example 
of this use of total reflection. 

The mirage (see Fig. 375) is an optical illusion by which distant 
objects, below the horizon, are sometimes plainly seen. This phe- 
nomenon is most frequently observed in hot, desert regions, when 
the air conditions are such that the lower strata near the ground are 
very much hotter than those above. These lower strata, having ex- 
panded the most, are less dense than the cooler ones above. Hence 
a ray of light traveling obliquely downward is refracted more and 
more until total reflection takes place. The images seen are inverted 



LIGHT 415 

giving a representation of trees or other objects reflected on the sur- 
face of still water. The mirage is also frequently seen at sea, ships 
being observed, sometimes erect, sometimes inverted, apparently sail- 
ing in the clouds near the horizon. Over the Great Lakes, trees, boats, 




Fig. 375. Diagram of a mirage. 

and towns on the opposite shore, sixty or seventy miles away, 
can sometimes be plainly seen, apparently but a few miles out. In 
this case the images are erect, the total reflection being from warm, 
still layers of air over colder layers near the water. 

Important Topics 

(A) Refraction: cause, illustration, two principles. 

(B) Index of refraction, meaning. 

(C) Plates, prisms, lenses, action of each. 

(D) Total reflection, uses. 

Exercises 

1. Compute the speed of light in water, the index of refraction 
being 1.33. 

2. If one wished to shoot a fish under water, should he aim at the 
apparent location of the fish as viewed from the air? Explain, 
using a diagram. 

3. Define refraction. Mention two illustrations of this action 
that you have observed out of school. 

4. Why does the moon look larger near the horizon? 

5. Is your reflection seen in a pool of water upside down? Why? 

6. Why does it whiten molasses candy to pull it? 

7. When looking at a building through the ordinary glass of a 
window why do straight lines of the building appear to be so 
distorted? What makes them appear to move as you move 
your head slightly? 



41 6 . PHYSICS 

8. Explain the phenomenon which one observes when looking at 
an object through the air arising from a hot stove or radiator. 

9. Frequently the horizontal diameter of the setting sun appears 
be greater than the vertical. Explain. 

10. Explain why one observes several images of a luminous body 
like a lighted candle when the reflected light from a thick glass 
mirror enters the eye, the angle of reflection being large. 

(5) The Formation of Images by Lenses 

382. Uses of Lenses in Optical Instruments. The use 

of instruments that employ lenses in their operation, such 
as spectacles, reading and opera glasses, and the camera, 
microscope, and telescope, is familiar to most students of 
physics. The part played by the lenses, however, is not 
generally understood. Consequently the study of the 
formation of images by lenses is of general* interest and 
importance. 

383. Forms of Lenses. While a lens may be formed 
from any transparent solid it is commonly made of glass. 

It may have two curved surfaces or 

one curved and one plane surface. 

Most lenses are spherical lenses, since 

their curved surfaces form a part of 

the surface of a sphere. Fig. 376 

represents a spherical lens with a 

Fig. 376?^Formation curved surface coinciding with that of 

of a s P herical lens - a sphere whose center is at C This 

center is called the center of curvature, while the radius of 

the sphere R, is the radius of curvature. 

There are two classes of lenses : those thick in the middle 
are called convex, while those thick at the edges are concave. 
The mode of constructing the six forms of spherical lenses 
is shown in Fig. 377. These are named as follows: (1) 
double convex, (2) piano convex, (3) concavo-convex, 
(4) double concave, (5) planoconcave, (6) convexo-concave. 




LIGHT 



417 



384. Effect of Lenses upon Light. The most important 
characteristic of a lens is its effect upon a beam of light. 
Most persons have seen a "burning glass," a double convex 
lens, used to bring to a point, or focus, a beam of sunlight. 
To show the action of a burning glass send a beam of 



\1 



\2 



\3 




\4 



)5 



;6 



Fig. 377. Forms of Lenses. 1. double convex; 2. piano convex: 
3. concavo convex; 4. double concave; 5. piano concave; 6. convexo 
concave. 

light into a darkened room, and place in its path a double 
convex lens. (See Fig. 378.) If two blackboard erasers 
are struck together near the lens, the chalk particles in the 
path of the light are strongly illuminated, showing that the 
light after passing through the lens it brought to a focus 
and that it spreads out beyond this point. This point 




Fig. 378. The action of a burning glass. 

to which the cone of light rays converges after passing 
through the convex lens is called the principal focus of 
the lens. The distance from the principal focus to the 
center of the lens is the focal length or principal focal 
distance of the lens. The focal length of double convex 

27 



4i8 



PHYSICS 




lenses of crown glass is about the same as the radius of 
curvature of either surface. The action of a convex or 
converging lens upon light may be better understood by 
studying Fig. 379 in which light is passing from S to F. 

The successive positions and 
shape of the advancing light 
waves are indicated by lines 
drawn across the beam. The 
light being retarded more in 
the thicker part of the lens, 
the light waves on leaving 
the lens have a concave front. 
Since light waves tend to move at right angles to the front 
of the wave, the light is brought to a focus. After pass- 
ing the focus the waves have a convex front, forming a 
diverging cone. 

385. Concave Lenses. When sunlight passes through 
a concave lens a diverging cone of light is formed. (See 
Fig. 380.) This is caused by the edges of the wave being 
retarded more than the center, producing a convex wave 
front. This diverging cone of light acts as if it had pro- 
ceeded from a luminous point at F. 



Fig. 379. Wave diagram of 
light passing through a convex 
lens. 




Fig. 380. Wave diagram of light passing through a concave lens. 

This point is called a virtual focus and is nearly at the 
center of the curvature of the nearer surface. 

386. The Formation of Images by Lenses. If a beam 
composed of parallel rays of light, as sunlight, is sent in 



LIGHT 



419 



turn through three convex lenses of the same diameter but 
of different thickness, it is 
found that the thicker the 
lens the greater is its converg- 
ing power, or the shorter is its 
focal length. (See Fig. 381.) 
Now if a luminous body, 
such as a lighted candle, be 
placed near the convex lens 
but beyond its local length, 
the light will be brought to a 
focus upon the other side of 
the lens and an image of the 
candle may be clearly seen 
upon the screen placed at 
this point. (See Fig. 382.) 
The two points so situated on 
opposite sides of a lens that 
an object at one will jorm an image at the other arc called 
conjugate foci. 

It will be helpful to compare the images formed of a 




Fig. 381. The thicker the lens, 
the shorter is its focal length. 




Fig. 382. C and S are at conjugate foci. 

candle by an aperture and by a convex lens. Rays of 
light from each point of the luminous body pass through 



420 PHYSICS 

the aperture in straight lines and produce upon the screen 
a lighted space of the same shape as the candle. This 
image is rather hazy in outline. Each cone of rays from 
luminous points of the flame is brought by the lens to a 
focus on the screen, producing a sharp image. It is the 
converging power of convex lenses that enables them to 
produce clear images. 

387. The Construction of Diagrams to Represent the 
Formation of Images by Lenses. Just as the earth has 
an axis at right angles to its equator to which are referred 
positions and distances, so a lens has a principal axis at 




Fig. 383. Construction of a real image by a convex lens 

right angles to its greatest diameter and along this axis 
are certain definite positions as shown in Fig. 383. Let 
MN be the principal axis of a convex lens, P and P' are 
principal foci on either side of the lens, S and S' are 
secondary foci. These are at points on the principal axis 
that are twice as far from O, the center of the lens, as are 
the principal foci. In the formation of images by a convex 
lens, several distinct cases may be noticed: 

(A) If a luminous body is at a great distance at the left, 
its light is brought to a focus at P, or its image is formed 
at P. (B) As the object approaches the lens the image 
gradually recedes until the object and image are at S and 
S', equally distant from O and of equal size (as in Fig. 383). 
The object and image are now said to be at the secondary 
foci of the lens. (C) As the object moves from S to P the 
image recedes, rapidly increasing in size until (D) when 



LIGHT 



421 



the object is at P the rays become parallel and no image 
is formed. (E) When the object is between P and the 
lens, the rays appear to proceed from points lack of the 
object, thus forming an erect, larger, virtual image of the 
object. (See Fig. 384.) This last arrangement illustrates 
the simple microscope. 




Fig. 384. Construction of a virtual image by a convex lens. 

With a concave lens but one case is possible, that cor- 
responding to the one last mentioned with convex lenses; 
since the rays from a body are divergent after passing 
through a concave lens they appear to proceed from points 
nearer the lens than the object and hence a virtual, erect, 




Fig. 385. Construction of a virtual image by a concave lens. 

smaller image of the object is formed. This virtual image 
may be seen by looking through the lens toward the object. 
(See Fig. 385.) 

388. The Lens Equation. The location of either the 
object or of the image upon the principal axis of the lens 
may be calculated if the position of one of these and the 



422 PHYSICS 

focal length are known. This is accomplished by the use 

of a formula ^ = ^r + -=- in which F represents the focal 

length and D and Di the distance from the lens of the 
object and the image respectively. Thus if an object is 
placed 30 cm. from a lens of 10 cm. focal length, where will 

the image be formed? Thus: = h -p.' and 3.D1 = 

G 10 30 D 

Di + 30, or 2D1 = 30 Z>i = 15. This result indicates 

that a real image will be 15 cm. from the lens. A minus 

value would indicate a virtual image. 

Important Topics 

(A) Lenses: convex, concave, six forms, center and radius of 
curvature. 

(B) Principal focus, focal length, virtual focus, conjugate foci. 

(C) Principal axis, images formed when object is in various locations. 

(D) Computation of location of images. 

Exercises 

1. Why is an image of a candle formed by an aperture, not sharply 
defined? 

2. When a photographer takes your picture and moves the camera 
nearer you, must he move the ground glass screen toward the 
the lens or away from it? Explain. 

3. How can you find the principal focal length of a lens? ' 

4. How can you test a spectacle lens to see whether it is convex 
concave? 

5. When will a convex lens produce a virtual image? Have you 
ever seen one? Where? 

6. When a photographer wishes to obtain a full length view of a 
person, where does he place the camera? 

7. The focal length of the lens is 24 cm. How far from the lens 
must an object be placed in order that a real image may be 
three times as long as the object? 

8. There is a perfect image of an object on the ground glass of a 
camera. The center of the lens is 20 cm. in front of the image 



LIGHT 



423 



and the object 75 cm. from the lens. What is the focal length of 
the lens? 
9. An object is 60 cm. from the lens, the image 120 cm. from it. 
Find the focal length. 

10. How can you find experimentally the principal focal length 
of a lens? 

11. A lens is used to project an enlarged image of a candle upon a 
screen. Which is farther from the lens, the candle or the image? 
Explain. 

(6) Optical Instruments 

389. The Eye. The most common optical instrument 
is the eye. While the structure of the eye it complicated, 
the principle of it is simple, involving the formation of an 
image by a double convex lens. 
(See Fig . 3 8 6 , in which is shown 
a front to back, vertical cross- 
section of the eye.) The eye 
appears to be made of portions 
of two spheres, one of which, 
smaller than the other, is 
placed in front. This pro- 
jecting part is transparent, 
but refracts the light which 
strikes it obliquely, so as to turn it into the eye. This 
enables us to see objects at the side when looking 
straight ahead. Test this by looking directly in front of 
you and see how far back on each side of the head you can 
notice a movement of the forefinger of each hand. 

390. Action of the Eye in Vision. When we look at an 
object, a small, real, inverted image is formed upon the 
retina at the back of the interior of the eye. The retina is 
an expansion of the optic nerve and covers the inner sur- 
face at the back of the eyeball. Seeing is due to the action 
of light in forming images upon the retina. Our eyes are 
so constructed that when they are relaxed the lens is ad- 




Fig. 386. Cross-section of 
the eye. 



424 PHYSICS 

justed to form clear images of distant objects upon the 
retina. If we look from distant to near objects without 
changing the shape of the eye lens, a sharp image of the 
latter cannot be formed and we get a blurred impression. 
It is difficult, however, to look at objects without automat- 
ically adjusting the eye lens so that it will make a sharp 
image. Test this by looking out of a window at a distant 
object, then without moving the head or eyes look at the 
glass of the window; you will notice a slight change of some 
sort in the eye itself as the vision is adjusted. This adjust- 
ment is made by muscles that pull or compress the eye lens 
so as to make it thicker for near objects and thinner for 
distant ones. The eye ordinarily does not see objects 
nearer than 10 in. clearly. This means that the greatest 
possible thickening of lens will not form clear images upon 
the retina if the object is nearer than 10 in. (25 cm.). 

391. The Visual Angle. To examine objects carefully 
we usually bring them as close to the eye as possible, for 

the nearer to the eye the 
si yf object is brought, the larger 

is the visual angle formed 
by it (see Fig. 387), and the 








% gt larger is its image upon the 

Fig. 3 8 7 .-The visual angle, AOB retina ; Tke ual angle of 

is greater at AB than at A'B'. an object is the angle at the 

eye lens between the rays that 
have come from the ends of the object. Consequently the more 
distant the object, the smaller is its visual angle. Now if we 
wish to examine small objects with great care, we frequently 
find that it is necessary to bring them close to the eye so 
that they have a visual angle of adequate size. If they 
must be brought closer than 10 in. a double convex lens 
is placed in front of the eye. This assists the eye lens in 
converging the light so that a clear image may be formed 



LIGHT 



425 



D 




Fig. 388.- 



-Action of the simple 
microscope. 



when the object is close, say an inch or so from the eye. 
This is the principle of the magnifying glass used by watch- 
makers and of the simple microscope. The action of the 
latter is illustrated by Fig. 388. The convex lens forms 
a virtual, enlarged im- 
age "A'-B"' of the ob- 
ject "A-B" which it 
observed instead of the 
object itself. 

392. Defects of Vis- 
ion. There are several 
defects of vision that 
may be corrected by 
spectacles or eye- 
glasses. One of these is "near-sightedness." It is due 
either to an eyeball that is elongated, or to an eye lens that 
is too convex, or to both conditions. This condition brings 
light from distant objects to a focus too soon (as shown in 
Fig. 389). Only light from near objects will focus upon 
the retina in such cases. With normal vision light from 
distant or near objects may be focused without unusual 

effort upon the retina, see 
Fig. 390. The remedy for 
near-sightedness is to use 
concave lenses which will 
assist in properly refracting 
the light so the focus will be 
formed on the retina (Fig. 
391). " Far-sightedness " is 
me reverse of near-sightedness; the eyeball is either too 
short, or the lens too flat, or both conditions obtain, so 
that the light entering the eye is brought to a focus behind 
the eyeball (Fig. 392) . The remedy is convex lenses which 
will assist in properly converging the light, see Fig. 393. A 




Fig. 389. " Near sightedness, or 
myopia. Parallel rays come to a 
focus at jF; emerging rays focus at 
A, the far point. 



426 



PHYSICS 



third defect is called astigmatism. This is caused by some 
irregularity or lack of symmetry in the eye. It is corrected 




Fig. 390. The normal eye. The parallel rays A B focus without ac- 
commodative effort at C. 




Fig. 391. Correction of near- 
sightedness by concave lens. 



Fig. 392". Far-sightedness or 
hyperopia. Parallel rays focused 
behind the retina. 



by a cylindrical lens that compensates for this defect of 
the eye. A diagram similar to Fig. 394 is used as a test 
for astigmatism. If the lines 
appear with unequal distinct- 
ness, some irregularity of re- 
fraction (astigmatism) is indi- 
cated. 
393. The Photographic Cam- 





Fig. 393. Correction of far-sighted- 
ness by a convex lens. 



Fig. 394. Test card for 
astigmatism. 



era. This is a light-tight box, provided with a convex 
lens in front, covering an aperture and a ground glass 



LIGHT 



427 



screen at the back. The distance between the lens and 
the screen is adjusted until a sharp image is obtained 
upon the latter, which is then replaced by a sensitive 
plate or film. The sensitized surface of the plate or film 
contains a salt of silver which is changed by the action of 
light. After the plate has been "exposed" to the action 
of light, it is "developed" by the use of chemicals pro- 
ducing a negative image. From "negative," by the use 
of sensitized paper, "positive" prints may be secured 
which resemble the object photographed. 

394. The projecting lantern (see Fig. 395) employs a 
strong source of light, as an electric arc lamp L, to strongly 




Fig. 395. Diagram of the projecting lantern. 



illuminate a transparent picture, or lantern slide, S, a real 
image (/) of which is formed upon a large screen. Two 
large plane-convex lenses (C), called condensing lenses, 
are placed near the lamp to concentrate the light upon the 
"slide" S. The convex lens forming the image is called 
the "objective" (0). 

395. The compound microscope consists of two lenses. 
One called the objective is placed near the object to be 
viewed. This lens has a short focal length usually less 
than a centimeter. It forms a real image of the object. 
A'-B' . The other lens, the eyepiece forms a virtual image 
of this real image. A"-B" ' . (See Fig. 396.) 



428 



PHYSICS 



396. The telescope consists of two lenses, the eyepiece 
and the objective. As in the compound microscope, the 
objective of the telescope forms a real image of the distant 
object, the eyepiece forming an enlarged virtual image of 
the real image. It is the virtual image that is viewed by 

5* IK 




Fig. 396. Formation of an image by a microscope. A-B is the object. 
B'-A' the real image formed by the "objective." B"-A"'is> the virtual 
image formed by the eyepiece. The eye sees the virtual image. 

the observer. (See Fig. 397.) In order to collect sufficient 
light from distant stars the objective is made large, some- 
times 50 in. in diameter. 

The length of the telescope tube depends upon the. 
focal length of the objective, since the distance between 
the two lenses must equal the sum of their focal lengths. 

O 

c 




D 

Fig. 397. Formation of an image by a telescope, b-a is the real image; 
d-c is the virtual image seen by the observer. 

397. The opera glass consists of a convex lens as objec- 
tive and a concave lens as an eyepiece. The former tends 
to form a real image but the latter diverges the rays before 
a real image can be formed, the action of the two lenses 
producing an enlarged virtual image (as in Fig. 398) which 



LIGHT 



429 



is viewed by the one using the glass. The compact size 
of the opera glass is due to the fact that the distance 
between the two lenses is the difference of the focal lengths. 




Fig. 398. Formation of an image by an opera-glass, a-b is the virtual 

image. 

398. The Prism Field Glass or Binocular . This instru- 
ment has come into use in recent years. It possesses the 
wide field of view of the spy glass but is as compact as the 
opera glass. This compact form is secured by causing the 
light to pass back and forth between two right-angle 




Fig. 399. Diagram of the Zies binocular or prism field glass. 

prisms (as shown in Fig. 399). This device permits the 
use of an objective lens with a focal length three times 
that of the tube, securing much greater magnifying power 
than the short instrument would otherwise possess. A 
further advantage is secured by the total reflection from 



430 PHYSICS 

the two prisms, one of which is placed so as to reverse the 
image right for left and the other inverts it, so that when 
viewed in the eyepiece it is in its proper position. 

Important Topics 

i. The eye: parts, formation of image, kind, how, where. 

2. Eye defects, how remedied. Visual angle. 

3. Simple microscope, camera; images, kind, how formed. 

4. Compound microscope, telescope and opera glass; images, action 
of each lens. 

Exercises 

1. Name three instruments in which lenses form virtual images 
and three in which real images are formed. 

2. In what direction is an oar in water apparently bent? Explain 
by a diagram. 

3. What optical instruments have you used? Is the visible image 
formed by each of these real or virtual? 

4. The focal length of a copying camera lens is 14 in. Where must 
a drawing be placed so that an image of the same size may be 
formed upon the ground glass screen? What must be the dis- 
tance of the screen from the lens? 

5. What are two methods by which you can determine the focal 
lengths of the lens of a photographic camera? 

6. The critical angle for water is 48)^ degrees. Show by a dia- 
gram how much of the sky can be seen by a diver who looks 
upward through the water. 

7. How is near-sightedness caused? How is it corrected? Illus- 
trate by a diagram. 

8. How is the eye accommodated (focused) as an object gradually 
approaches it? 

9. Explain why a simple microscope assists in looking at the parts 
of a flower or insect. 

10. Why do people who have good eyesight when young require 
glasses as they grow old? 

(7) Color and Spectra 

399. Color. Much of the pleasure experienced in gazing 
at beautiful objects is due to the color shown by them. 



Guglielmo Marconi (Italy) . In- 
ventor of wireless telegraphy. 





Gtjglielmo Marconi 
Copyright by Underwood & Under- 
wood, N. Y." 



Alexander Graham Bell, Washing- 
ton, D. C. Inventor of the tele- 
phone. 



Alexander Graham Bell 

"Copyright by Underwood & 

Underwood, N. Y." 



LIGHT 



433 



The blue sky, the green grass, and the varied tints of flowers, 
and of the rainbow all excite our admiration The study 
of color begins naturally with the production of the spec- 




Fig. 400. Formation of the spectrum by a prism. 

trum, the many-colored image upon a screen produced by 
passing a beam of light through a prism. The spectrum 
is best shown when the light enters by a narrow slit (Fig. 
400). The spectrum was first produced by Sir Isaac 
Newton in 1675 by the means just described. The names 
usually given to the more prominent colors of the spectrum 
are violet, indigo, blue, green, yellow, orange, and red. 
The initials of these names, combined, spell vibgyor, a 
word without meaning except to assist in remembering the 
order of the colors in a spec- 
trum. If the light that has 
passed through a prism is sent 
through a second prism placed 
in reverse position (see Fig. 
401), the light passing through 
both prisms is found to be 
white. This experiment 
indicates that white light is composed of light of all colors. 
400. Dispersion. The separation of the colors by a 
prism is called dispersion. In experimenting to find a 

28 




Fig. 401. The colors of the 
spectrum recombine to form 
white light. 



434 PHYSICS 

reason for dispersion, it has been learned that lights of 
different colors are of different wave lengths. Color in 
light is therefore analogous to pitch in sound. We hear 
through many octaves, but we see through about one 
octave. That is, the shortest visible waves of violet 
light are about 0.000038 cm. in length while the longest 
visible red rays are 0.000076 cm., or the longest visible 
light waves are about twice the length of the shortest 
visible ones. It appears from the evidence of experiments 

upon dispersion that light 
waves of different lengths 
are refracted differently. 
This causes the images 
formed by refraction 
through simple glass lenses 
to be fringed with color 
and to lose some of their 
sharpness and definiteness 

Fig. 402. Violet light comes to a r . .-, 1 . 

focus sooner than red. of Outline, Since the Violet 

light is brought to a focus 
sooner than the red. (See Fig. 402.) This seriously affects 
the value of such lenses for optical purposes. Fortunately 
it is found that different kinds of glass have a different rate 
of dispersion for the same amount of refraction. 

401. The Achromatic Lens. The existence of these 
different kinds of glass makes possible a combination of 
lenses in which dispersion is entirely overcome with the 
loss of only about one-half of the refraction. Such a com- 
bination is shown in Fig. 403. It is called an achro- 
matic lens, since images formed by it are not colored 
but white (a = without, chroma = color) . The achromatic 
lens consists of a double convex- lens of crown glass combined 
with a plano-concave lens of flint glass. Achromatic lenses 
are used in all high-grade optical instruments such as 




LIGHT 435 

telescopes and microscopes. The colored images that are 
sometimes seen in cheap opera glasses show the result of 
not using achromatic lenses. 




Fig. 403. An achromatic lens. C is of crown glass; F, of flint glass. 

402. The Color of Bodies. Project the spectrum of 
sunlight upon a white surface in a darkened room. 

Now place in different parts of the spectrum objects of various 
colors. Red objects will show brilliant red when at the red end of 
the spectrum but look black at the blue end, while blue objects 
appear blue only at the blue end. 

These facts indicate that the color of an object depends 
upon two things: (a) the light that falls upon it and (b) the 
light which it sends to the eye, A black surface absorbs all 
color while a white one reflects all wave lengths to the eye 
in the same proportion that they come to it. A white 
object will appear red in red light, and blue in blue light 
since it reflects both of these. A colored object reflects 
light of its own color but absorbs all others. The color 
then of a body is due to the light which it does not absorb, 
but which comes from it to the eye. 

403. The color of transparent bodies, such as colored 
glass, is due to the presence of a dye or pigment contained in 
the body. This pigment absorbs a part of the light, the 
part transmitted giving the color. This may be shown by 
holding a sheet of colored glass in a beam of light either 
before or after it has passed through a prism. Some 
colors, as red, may be found to be nearly pure, only the 
red passing through, while green glass often transmits in 
addition to the green some yellow and some red light. 



436 PHYSICS 

404. Complementary Colors. If two prisms are placed 
in reversed position near each other (see Fig. 401) , a beam 
of light dispersed by one is recombined into white light 
by the other. If now a card is held between the two prisms 
so as to cut off some of the colored light, say the red, the 
remaining light will be found to form a greenish blue. If 
the card is removed, the light becomes white again. That 
is, red and peacock blue light together form white. Any 
two colors that together form white light are called com- 
plementary. Other complementary colors are light yellow 
and blue, green and crimson, orange and greenish blue, 
violet and greenish yellow. We must not confuse the 
combining of colors (light) and the combining of pigments, 
the latter consisting of bodies that absorb light. Yellow 
pigment absorbs all but yellow and some green, while 
blue pigment absorbs all but blue and some green. Mix- 
ing these two pigments causes the absorption of all 
colors but green. Blue and yellow paint mixed produce 
green, while blue and yellow light give white. 

405. The solar spectrum, as the spectrum of sun- 
light is called, may be observed in the rainbow. The 
latter is produced through the dispersion of light by spher- 
ical raindrops. Its formation may be imitated by sending 
a small circular beam of light through a screen against a 
round glass flask filled with water. (See Fig. 404.) The 
light passes through the water and is dispersed when 
it enters and when it leaves, producing a color upon the 

.screen at R-V. The course of the light within the drop 
is indicated in Fig. 405. The violet ray comes to the 
eye more nearly horizontal and is therefore below red, as 
we look at the rainbow. 

406. Fraunhofer Lines. Some of the most important 
features of the solar spectrum are not seen in the rainbow 
or in the band of light usually observed upon a screen. 



LIGHT 



437 



By the use of a narrow slit and a convex lens to carefully 
focus the slit upon a white screen it is seen that the solar 
spectrum is crossed by many dark lines. These are called 




Fig. 404. A rainbow formed by a beam of light striking a flask of water. 




Fig. 405. The course of a beam of light within a drop of water. 

Fraunhofer lines, to honor the German scientist who 
in 1 8 14 first accurately determined their position. Two 
experiments with a spectroscope will help to make clear the 
meaning of the Fraunhofer lines. 



438 PHYSICS 

407. The Spectroscope and Its Uses. The spectroscope 

(Fig. 406) is an instrument for observing spectra. It 

consists of a prism, a slit, and a convex lens T for focusing 

an image of the slit accurately upon a screen (Fig. 407) 

' where the spectrum is observed through the eyepiece E. 

(A) A Bunsen flame is placed in front of the slit and a 
heated platinum wire which has been dipped in common 
salt or some sodium compound placed in the Bunsen flame; 




Fig. 406. The spectroscope. 

the latter becomes yellow and a vivid yellow line is ob- 
served on the screen in the spectroscope. Other sub- 
stances, as barium and strontium salts, when heated to 
incandescence in the Bunsen flame, give characteristic 
bright lines. In fact each element has been found to have 
its own characteristic set of colored lines. This fact is 
made use of in spectrum analysis, by which the presence 
of certain elements in a substance can be definitely proved 
upon the appearance of its particular lines in the spectrum. 
(B) If light from, for example, an arc light is sent over a 
gas flame containing sodium vapor, a dark line appears in 



LIGHT 



439 



the spectrum in the exact position in which the yellow 
sodium line appeared. It seems that the sodium vapor 
removes from white light the same wave lengths that it it- 
self produces. This absorption is supposed to be due to 
sympathetic vibration ; just as a tuning fork it set in vibra- 




Fig. 407. Diagram of a spectroscope. 

tion by the waves of another fork in unison with it, at 
the same time absorbing the wave energy, so in the gas 
flame the sodium particles absorb the wave motion of the 
same vibration rate as that emitted by them. The fact 





Fig. 408. The bright line spectrum of iron and its coincidences with 
some of the dark lines of the solar spectrum. 



that the spectrum of sunlight contains a great many dark 
lines is believed to indicate that the sun is surrounded 
by clouds formed by the vaporization of the various sub- 
stances in the sun itself. By comparing the dark lines of 



44 PHYSICS 

the solar spectrum with the bright-line spectra of various 
substances found in the earth, such an exact correspon- 
dence of the lines is found that the presence of the vapor 
of these substances about the sun is considered proved. 
.(See Fig. 408 which shows the exact correspondence 
between the bright-line spectrum of iron vapor and the 
dark lines appearing in a portion of the sun's spectrum.) 
The spectra of the stars also contain certain dark lines. 
Thus the presence of the corresponding substances in dis- 
tant stars is considered as determined. 

408. Theory of Color Vision. By combining light of 
the three colors red, green and blue-violet in proper propor- 
tions, it has been found possible to produce any color 
effect, even white. This leads to the conclusion that in 
the retina of the eye are three different kinds or sets of 
sensitive nerve endings, sensitive respectively to red, to 
green, and to blue light. This idea is given corroboration 
by some facts of color blindness. Thus some persons have 
no sensation of red, this color not being distinguished 
from green. Others are color blind to green or blue. It 
is supposed that in color blind persons one of the sets of 
nerve endings sensitive to one of these three colors is 
lacking. 

409. Three-color Printing. Since all colors may be 
produced by mixing the three colors, light red, green, and 
blue-violet, these are called the three primary colors. The 
so-called primary pigments or paints are simply the com- 
plements of the three primary colors. They are, in order, 
peacock blue, crimson, and light yellow. The three 
pigments when mixed yield black, since combined they 
absorb all kinds of visible light. The process of three- 
color printing, now so generally employed in printing 
colored pictures for books, calendars, etc., consists in 
combining upon white paper three colored impressions, 



LIGHT 441 

using successively the three primary pigments (yellow, 
crimson and blue) from plates prepared as follows : 

Three photographs of a given colored object are taken, 
each through a different sheet of gelatine called a filter, 
stained the color of one of the primary colors. From these 
photographs half-tone blocks are made in the usual way. 
The colored picture is made by carefully superposing im- 
pressions from these blocks', using in each case an ink 
whose color is the complement of the "filter" through 
which the original picture was taken. An illustration of 
the process is given upon the plate in the frontispiece of 
this book. 

Important Topics 

1. Color, due to wave length; dispersion by prism, sphere in rain- 
bow, complementary colors, color of opaque and transparent 
bodies. 

2. Spectra, solar; formation of rainbow; bright-line spectra, how 
formed, how used; dark-line, how formed, used. 

3. Theory of color vision. Three color printing. 

Exercises 

1. How does a white flower look when viewed through a blue glass? 
Through a red glass? Through a red and blue glass at the same 
time? 

2. Why does a red ribbon appear black when seen by blue light and 
red when seen by red light ? 

3. In what part of the sky must you look to see a rainbow in the 
morning? In the afternoon? Explain. 

4. How would you arrange two similar prisms so as to produce 
double the deviation produced by one? 

5. The color of an object depends upon what two things? 

6. What kind of a spectrum should moonlight give? Why? 

7. A mixture of green and red lights gives a sensation of yellow. 
Can you suggest why a mixture of blue and yellow lights gives 
the sensation of white? 



442 PHYSICS 

(8) Nature of Light, Interference, Polarization 

410. The Corpuscular Theory. The theory of the 
nature of light that was most generally accepted until 
about the year 1800, held that light consists of streams of 
minute particles, called corpuscles, moving at enormous 
velocities. This corpuscular theory was in accord with the 
facts of reflection and the rectilinear motion of light, but 
was abandoned after the discovery of the interference of 
light, as it could not account for the latter phenomenon. 

411. The Wave Theory of Light. The theory that 
light is a form of wave motion was first advanced by Huy- 
gens, a Dutch physicist, in the seventeenth century. This 
theory was opposed at the start since (A) no medium was 
known to exist which would convey wave motion through 
space, as from the sun to the earth, and (B) the rectilinear 
motion of light was unlike that of any other form of known 
wave motions, such as that of water or of sound waves 
which are able to bend around corners. In answer to the 
first objection, Huygens assumed the presence of a medium 
which he named ether, while the second objection has been 
completely overcome during the past century by the dis- 
covery that light may deviate from a straight line. It is 
now known that the excessive shortness of light waves is 
the reason for its straight-line motion. Further, long ether 
waves, as those of wireless telegraphy, are found to bend 
around obstacles in a manner similar to those of water or 
sound. 

412. The interference of light is one of the phenomena 
for which the wave theory offers the only satisfactory 
explanation. Interference of light may be shown by tak- 
ing two pieces of plate glass and forcibly pressing them 
together by a screw clamp, as shown in Fig. 409. After a 
certain pressure has been reached, colored rings will appear 



LIGHT 



443 



about the compressed spot when viewed by light reflected 
from the upper surface of the glass. If light of one color, 
such as that transmitted by red glass, falls upon the appa- 
ratus, the rings are seen to be alternately red and dark 
bands. The explanation of this phenomenon according 
to the wave theory is as follows: The two sheets of glass, 
although tightly pressed together, are separated in most 
places by a thin wedge of air (see Fig. 410), which repre- 
sents in an exaggerated form the bending of the plates 



Destructive 
Interference 





Fig. 409. Two plates pressed Fig. 410. Illustrating the interference 
together by a screw clamp. of light by a thin film of air. 



when pressed by the clamp. Several waves are represented 
as coming from the right and entering the glass. Now the 
wave moving from R to the plates has some of its light re- 
flected from each glass surface. Consider the two portions 
of the wave reflected at each of the surfaces between the 
plates, i.e., from the two surfaces of the wedge of air. 
If the portion of the wave reflected from the second surface 
of the air wedge combines with that reflected from the 
first surface, in the same phase as at C, the two reflected 
waves strengthen each other. While if the two reflected 
portions of the wave meet in opposite phases as at A and B, 
a decrease or a complete extinction of the light results. 



444 physics 

This is called interference. If light of one wave length 
is used, as red light, the regions of reinforcement and inter- 
ference are shown by red and dark rings, while if white 
light is used, the ring where red light interferes, yields its 
complementary color, greenish blue. Where interference 
of greenish blue occurs, red is found, etc. Many phenom- 
ena are due to interference, such as (A) the color of thin 
films of oil on water, where the portions of light reflected 
from the two surfaces of the oil film interfere resulting in 
the production of color; (B) the color of soap bubbles. 
When first formed, soap-bubble films are not thin enough 
to show interference well, but as the bubbles increase in 
size or become thinner on standing, the conditions for 
interference are reached and, as the film becomes thinner, 
a regular succession of colors is noticed. 

413. Differences Between Light and Sound. Among 
the important differences between light and sound that 
have been considered are the following: the former are 
(a) waves in the ether, (b) of very short wave length, and 
(c) their motion is in straight lines. Another difference (d) 
is in the mode of vibration. 

Sound waves are longitudinal, while light waves are trans- 
verse. Light waves consist of vibrations of the ether at 
right angles to the line of motion. To illustrate the rea- 
soning that has led to this conclusion, suppose aropeto be 
passed through two vertical gratings. (See Fig. 411, 1.) 
If the rope be set in transverse vibration by a hand, the 
waves produced will readily pass through to the gratings 
P and Q and continue in the part extending beyond Q. 
If, however, Q is at right angles to P, no motion will 
be found beyond Q. Now if a stretched coiled spring with 
longitudinal vibrations should take the place of the rope, 
it is evident that the crossed position of the two gratings 
would offer no obstacles to the movement of the vibration. 



LIGHT 445 

In other words, crossed gratings offer no obstruction to 
longitudinal vibrations, while they may completely stop 
transverse vibrations. 








2 



Fig. 411. Transverse waves will pass through both gratings in (1) 
where the openings in the two gratings are at right angles. The waves 
passing P are stopped by Q (2). 

414. Polarization of Light. It is found that two crystals 
of tourmaline behave toward light just as the two gratings 
behave with respect to the transverse waves of the rope. 
Thus, if a small opening in a screen is covered with a 
tourmaline crystal, light comes through but slightly 
diminished in intensity. If a second crystal is placed over 
the first one so that the two axes are in the same direction 
as in Fig. 41 2P, light is as freely transmitted through the 
second crystal as through the first, but if the crystals are 
crossed (Fig. 4125) no light passes the second crystal. 





a 
a b b 

P S 

Fig. 412. Effect of tourmaline crystals on light. 

This experiment shows that the light which has passed 
through one tourmaline crystal will pass through another 
only when the latter is held in a certain position, hence it 
is believed that a tourmaline crystal is capable of transmit- 



446 physics 

ting light that is vibrating in one particular plane. The 
direct conclusion from this is that light waves are transverse 
rather than longitudinal. The exper ment just described 
illustrates what is called polarization of light. The beam 
that after passing through a (Fig. 412) is unable to pass 
through h, if the two axes are crossed; is called a polarized 
beam. The conclusion that light waves are transverse is 
therefore based upon the phenomenon of the po'ariza- 
tion of light. This was first discovered by Huygens in 
1690. 

Important Topics 

1. Interference of light: evidence, reasoning involved, illustration. 

2. Polarization of light: evidence, reasoning involved. 

3. Nature of light, differences between sound and light. 

Exercises 

1. Make a list of the differences between sound and light and state 
briefly the evidence upon which the knowledge of these differ- 
ences is based. 

2. Why will a thickness of film that will produce interference of 
red light be different from that producing interference for green 
or blue? 

v 

3. Using the formula n = : compute the vibration rate for violet 

light if its wave length is considered as 0.00004 cm. 

4. Explain how the fact of polarization affects the wave theory of 
light 

5. Show how it is possible by comparing the spectrum of the sun 
with that of a star to tell whether the star is approaching or 
receding from the earth. 

Review Outline : Light 

Light; speed, source, medium. 

Straight Line Motion; shadow, umbra, penumbra, eclipse, image. 
Photometry; Law of intensity, candle power, foot-candle. 
Mirrors; Law of reflection; image real, virtual ; plane, curved, para- 
bolic, mirrors. 



LIGHT 447 

Refraction; cause and effects; plate, prism, lens; total reflection. 

Lenses; sijc forms, principal focus, center, lens equation, i/F = i/D 
+ i/Di. 

Optical instruments; eye, defects and correction, camera, micro- 
scope, etc. 

Spectra; 3 kinds, dispersion, production of color effects, spectroscope, 
uses. 

Nature of Light; wave theory, interference, polarization, 
significance. 



CHAPTER XVII 



INVISIBLE RADIATIONS 

(i) Electric Waves and Radio-activity 

415. Oscillatory Nature of the Spark from a Leyden 
Jar. In studying sound (Art. 339), the sympathetic 
vibration of two tuning forks having the same rate of 
vibration was given as an illustration of resonance. The 
conditions for obtaining electrical resonance by the use of 
two Leyden jars are given in the following experiment. 

Join the two coats of a Leyden jar (Fig. 413) to a loop of wire L, 

the sliding crosspiece M 
P being arranged so that the 

length of the loop may be 
changed as desired. Also 
place a strip of tinfoil in 
contact with the inner coat- 
ing and bring it over to 
within about a millimeter 
of the outer coating as indi- 
cated at G. Now join the 
outer coating of another 
exactly similar jar A to a 
wire loop of fixed length, the end of the loop being separated from 
the knob connected to the inner coating, a short distance at P. 
Place the jars near each other with the wire loops parallel and con- 
nect coatings of A to the terminals of a static machine or an 
induction coil. At each discharge between the knobs at P, a spark 
will appear in the other jar at G, if the crosspiece M is so adjusted 
that the areas of the two loops are exactly equal. When the wire 
M is moved so as to make the areas of the two loops quite unequal, 
the spark at G disappears. 

The experiment just described shows that two electrical 
circuits can be tuned by adjusting" their lengths, just as 

448 




Fig. 413. 




INVISIBLE RADIATIONS 449 

two tuning forks may be made sympathetic by adjusting 
their lengths. This fact indicates that the discharge of 
the Leyden jar is oscillatory, since resonance can plainly 
not be secured except between bodies having natural 
periods of vibration. This same fact is also shown by 
examining the discharge of a Leyden jar as it appears when 
viewed in a rapidly revolving mirror. (See Fig. 414.) 
The appearance in the 
mirror shows that the dis- 
charge is made up of a 
number of sparks, often a 
dozen or more, vibrating 

11 1 r ,v . ,t Fig. 414. Photograph of the oscilla- 

back and forth until they tory discharge of a Leyden jar. 

finally come to rest. The 

time of one vibration varies from one millionth to one- 
hundred millionth of a second, depending on the space 
between the discharging balls and the size of the jars. 

The discharge of a Leyden jar or of another condenser 
sets up ether waves that have the speed of light. Hein- 
rich Hertz in Germany first proved this in 1888. These 
waves are now known as Hertzian waves. The length of 
these varies from 3 cm. to several miles, depending upon the 

size and conditions of 
T P P'J j \ T' the discharging circuit. 

(( ^mm& )) '416. The Coherer 

Fig. 41 5.-A coherer. The coherer is a device 

for detecting electric 
waves. It consists of a glass tube with metal filings 
loosely packed between two metal plugs that fit 
the tube closely. (See Fig. 415.) These filings offer a 
high resistance to the passage of an electric current, but 
when electric waves pass through the filings these cohere 
and allow a weak current to pass through. This cur- 



450 . PHYSICS 

rent may be strong enough to operate a relay connected 
with a sounder or bell that gives audible signals. If the 
tube be tapped the filings will be disturbed and the resis- 
tance again made so high that no current can pass through. 
417. Wireless Telegraphy. In 1894 Marconi, then a 
young man of twenty, while making some experiments 
with electrical discharges discovered that the coherer 
would detect electrical waves at a considerable distance 
from their source and that by the use of a telegraph key 
the "dots and dashes" of the telegraph code could be 
reproduced by a sounder attached to a relay. At present 
the coherer is used principally in laboratory apparatus, 
as much more sensitive detectors are now available for 
commercial work. The essential parts of a modern wire- 
less telegraph apparatus as used in many commercial 
stations are shown in Fig. 416. 

Alternating current at no volts is sent into the primary, P, of 
a transformer, the secondary, S, of which produces a potential of 
5000 to 20,000 volts. The secondary charges a condenser until 
its potential becomes high enough to produce a discharge across a 
spark gap, SG. This discharge is oscillatory, the frequency being 
at the rate of about one million a second, depending upon the 
capacity of the condenser and the induction of the circuit. 

These oscillations pass through the primary of the oscillation 
transformer, inducing in the secondary, electric oscillations which 
surge back and forth through the antennae, or aerial wires, A . These 
oscillations set up the "wireless waves." The production of these 
waves is explained as follows: An electric current in a wire sets up 
a magnetic field spreading out about the conductor; when the cur- 
rent stops the field returns to the conductor and disappears. The 
oscillations in the antennae, however, have such a high frequency, 
of the order of a million a second, that when one surge of electricity 
sets up a magnetic field, the reverse surge immediately following 
sets up an opposite magnetic field before the first field can return to 
the wire. Under these conditions a succession of oppositely directed 
magnetic fields are produced which move out from the antennae 



INVISIBLE RADIATIONS 



451 



with the speed of light and induce electric oscillations in any con- 
ductors cut by them. 




While the electric waves are radiated in all directions from the 
aerial, the length of the waves set up is approximately four times the 
combined length of the aerial wires and the "lead in" connection 
to the oscillation transformer. 



452 PHYSICS 

The electric waves induce effective electrical oscillations in the 
aerial of the receiving station, even at distances of hundreds of miles, 
provided the receiving transformer, RT, is " tuned " in resonance with 
the transmitting apparatus by adjustments of the variable con- 
denser, VC, and the loading coil, L. The detector of these oscil- 
lations in the receiving transformer is simply a crystal of silicon or 
carborundum, D, in series with two telephone receivers, Ph. The 
crystal detector permits the electric oscillations to pass through it 
in one direction only. If the crystal did not possess this property, 
the telephone could not be used as a receiver as it cannot respond 
to high frequency oscillations. While one spark passes at SG, an 
intermittent current passes through the receiver in one direction. 
Since some 300 to 1200 sparks pass each second at SG while the key, 
K, is closed, the operator at Ph hears a musical note of this fre- 
quency as long as K is depressed. Short and long tones then corre- 
spond to the dots and dashes of ordinary telegraphy. In order to 
maintain a uniform tone a rotary spark gap, as shown* is often used. 
This insures a tone of fixed pitch by making uniform the rate of 
producing sparks. 

The Continental instead of the Morse code of signals is 
generally employed in wireless telegraphy, since the former 
employs only dots and dashes. The latter code employs, 
in addition to dots and dashes, spaces which have some- 
times caused confusion in receiving wireless messages. 
The United States government has adopted the regulations 
of the International Radio Congress which directs that 
commercial companies shall use wave lengths between 
300 and 600 or above 1600 meters. Amateurs may use 
wave lengths less than 200 meters and no others, while the 
government reserves the right to wave lengths of 600 to 
1600 meters. See p. 459 for Continental telegraph code. 

418. Discharges in Rarefied Air. Fig. 417 represents 
a glass tube 60 or more centimeters long, attached to an 
air pump. Connect the ends of the tube to the terminals 
of a static machine or of an induction coil, a-b. At first 
no sparks will pass between a and /, because of the high 



INVISIBLE RADIATIONS 



453 



resistance of the air in the tube. Upon exhausting the air 
in the tube, however, the discharge begins to pass through 
it instead of between a and b. This shows that an elec- 
trical discharge will pass more readily through a partial 
vacuum than through air at ordinary pressure. As the 
air becomes more and 
more exhausted, the 
character of the discharge 
changes. At first it is a 
faint spark, gradually 
changing until it be- 
comes a glow extending 



a b 





g l 



Fig. 417. An Aurora tube. 



from one terminal to the other and nearly filling the 
tube. 

Geissler tubes are tubes like the above. They are 
usually made of different kinds of glass twisted into various 
shapes to produce beautiful color effects. The aurora 
borealis or northern light is supposed to be electric dis- 



1 










; 




iP^^B^f* S 


HHP^i. ' 





Fig. 418. Aurora Borealis. 

charges through rarefied air at the height of from 60 to 
100 miles above the earth's magnetic poles. (See Fig.418.) 
419. Cathode Rays. When the tube in Art. 420 is 
exhausted to a pressure of 0.001 mm., or a little less than 
one millionth of an atmosphere, the character of the dis- 




454, PHYSICS 

charge is entirely changed. The tube becomes filled with 
a yellowish green phosphorescent light. This is produced 
by what are called cathode rays striking the glass walls of 
the tube. These rays are called 
cathode rays because they come 
from the cathode of the tube. 
They are invisible and that they 
travel in straight lines is shown 
by the shadow obtained by using 
a tube with a screen (Fig. 419). 
Fig. 419.-A cathode ray 420 x Rays. In 1895, Pro- 
fessor Rontgen of Wurtzburg, 
Germany, discovered that when the cathode rays strike 
the walls of the tube or any solid within it they excite 
a form of invisible radiation. This radiation is called 
Rontgen rays, or more commonly, "X" rays. Careful 
experiments show that they travel in straight lines, and 
that they can not be reflected or refracted as light waves 
are. They pass through glass and opaque objects such 
as flesh, cardboard, cloth, leather, etc., but not through 
metallic substances. The tube in Fig. 420 has a screen 
covered with crystals which become luminous when struck 
by . the cathode rays. On bringing a magnet near the 
tube the luminous line is raised or lowered showing that 
the magnetic field affects the stream of cathode rays, 
attracting it when in one position but repelling it when in 
the reverse direction. The cathode rays which cause the 
bright line possess a negative charge of electricity. They 
are now believed to be electrons shot off from the surface 
of the cathode with speeds that may reach 100,000 miles 
a second. " X " rays possess no electrical charge whatever 
and cannot be deflected by a magnet. They produce the 
same effect on a photograph plate as light does, only more 
slowly. Hence, they can be used in taking "X" ray 



INVISIBLE RADIATIONS 



455 



photographs. Certain crystals, like barium platinum 
cyanide, fluoresce when struck by the "X" rays. The 




Fig. 420. The stream of cathode Fig. 421. A fluoroscope. 
rays is deflected by a magnet. 




Fig. 422. A view of the "shadow" of a hand as seen in a fluoroscope. 



fluoroscope is the name given to a light-tight box closed at 
one end by a cardboard covered with these crystals (Fig. 



456 physics 

421). On looking into the fluoroscope with an opaque 
object such as the hand placed between the screen and 
the "X" ray tube, a shadow of the bones of the hand can 
be seen upon the screen of the fluoroscope. (See Fig. 422.) 
A special form of the tube is used. (See Fig. 423.) In 
this tube a platinum disc is placed at the focus of the con- 
cave cathode. This concentrates the "X" rays in one 
^-g-pr^ direction. It is now generally 

^4fw\ believed that "X" rays are 

jjf^ >P + waves in the ether set up by 
I the sudden stoppage of the 

^^^^^^^MkU- cathode rays at the platinum 

/JV^^^% 4 2I The Electromagnetic 

$^ Theory of Light. The study 

of electric waves has shown 

Fig. 4 23.-An "X" ray tube. ^ ^ ^ ^^^ tQ ^ 

waves in many respects: (a) they have the same velocity; 
(b) they can be reflected and refracted. The main differ- 
ence is in their length, light waves being very much shorter. 
In 1864 James Clark Maxwell, an English physicist, pro- 
posed the theory that ether waves could be produced by 
electrical means and that light waves are electromagnetic. 
In 1888 Hertz proved by his experiments that ether waves 
having the same velocity as light could be produced in 
this way. It is now the general belief that light waves 
are ether waves produced by the vibrations of the elec- 
trons within the atoms and that they consist of electro- 
magnetic waves in the ether. 

422. Radio-activity. In 1896 Henri Becquerel of Paris 
discovered that uranium and its compounds emit a form 
of radiation, that produces an effect upon a photographic 
plate that is similar to that resulting from the action of 
"X" rays. These rays are often called Becquerel rays in 



INVISIBLE RADIATIONS 457 

honor of their discoverer. The property of emitting such 
rays is called radio-activity, and the substances producing 
them are called radio-active. 

In 1898, Professor and Mme. Curie after an investigation 
of all the elements found that thorium, one of the chief 
constituents of incandescent gas mantles, together with its 
compounds, was also radio-active. This may be shown 
by the following experiment: 

Place a flattened gas mantle upon a photographic plate and leave 
in a light tight-box for several days. Upon developing the plate in 
the usual way a distinct image of the mantle will be found upon the 
plate. 

423. Radium. Mme. Curie discovered also that pitch- 
blende possessed much greater radio-active power than 
either thorium or uranium. After prolonged chemical 
experiments she obtained from several tons of the ore a 
few milligrams of a substance more than a million times 
as active as thorium or uranium. She called this new 
substance radium. Radium is continually being decom- 
posed, this decomposition being accompanied by the 
production of a great deal of heat. It has been calculated 
that it will take about 300 years for a particle of radium 
to be entirely decomposed and separated into other sub- 
stances. It is also believed that radium itself is the 
product of the decomposition of uranium, atomic weight 
238, and that the final product of successive decomposi- 
tions may be some inert metal, like lead, atomic weight 
207. 

The radiation given off by radio-active substances con- 
sists of three kinds: (A) Positively charged particles of 
helium called alpha rays: (B) negatively charged particles 
called beta rays: (C) gamma rays. 

The alpha rays have little penetrating power, a sheet 




458 PHYSICS 

of paper or a sheet of aluminum 0.05 mm. stopping them. 
Upon losing their charges they become atoms of helium. 
"Their velocity is about }{ of that of light or 18,000 miles 
a second. The spinthariscope is a little instrument devised 
by Sir Williams Crookes in 1903 to show direct evidence 
that particles are continually being shot off from radium. 
In this instrument (Fig. 424), a speck of radium R is 
placed on the under side of a wire placed a 
few millimeters above a screen S covered 
with crystals of zinc sulphide. Looking in 
the dark at this screen through the lens L, 
a continuous succession of sparks is seen 
like a swarm of fireflies on a warm summer 
night. Each flash is due to an alpha particle 
F S pinihlris 4 co7e A striking the screen. The beta rays are 
supposed to be cathode rays or electrons 
with velocities of from 40,000 to 170,000 miles a second. 
The gamma rays are supposed to be "X" rays produced 
by the beta rays striking solid objects. 

424. The discovery of radio-activity has revolutionized 
the ideas of the constitution of matter. Further, the 
results of experiments upon radio-active materials reveals 
the presence of immense quantities of sub-atomic energy. 
If man ever discovers a means of utilizing this, he will 
enter a storehouse of energy of far greater extent and 
value than any of which he has as yet made use. A 
consideration of this unexplored region gives zest to the 
work of those who day by day are striving to understand 
and control forces of nature. 

Important Topics 

1. Oscillatory nature of discharge of Leyden jar. Proofs. 

2. Wireless telegraphy and telephony. 

3. Electrical discharges in rarefied gases. 



INVISIBLE RADIATIONS 459 



4. Cathode and "X" rays. 

5. Electromagnetic theory of light. 

6. Radio activity and radium. 



CONTINENTAL TELEGRAPH CODE 



A ._ 
B __. . . 

D 

E . 


K 

L 

N 




s .. . 
T _ 

U 

V 

W 


F 


____ 




X 


G 


P 




Y _ . __ . 


H 

I .. 

Pbriod 


R. _. 

Interrogation 




Z 

Exclamation 




2 . . __ _ . 




3 


4 


5 6 





7 _ . . . 


8 


9 


. 





CHAPTER XVIII 

WIRELESS TELEPHONY AND ALTERNATING 
CURRENTS 

The developments in Wireless communication have been so rapid 
during recent years that a more extended account, than that given 
in Art. 417 of the apparatus and methods used at the present time, 
seems desirable. The study of Alternating Currents is also included 
with the idea that it will make the text more complete and of 
wider usefulness. 

Wireless Telephony 

425. The Wireless Telephone. One of the most 
important developments in wireless communication in 
recent years has been in wireless telephony. We realize 
its possibilities, when we hear of the achievements 
of talking across an ocean or between airplanes and the 
ground. 

The wireless telephone can be best understood by 
comparing it with the common telephone. When the 
latter is in use, a direct current flows continually through 
the instrument. (See Arts. 312-316.) When a person 
speaks into the transmitter, the sound waves of the voice 
cause the diaphragm to vibrate, this action causes rapid 
changes in the resistance of the transmitter, which in turn 
causes the direct current to fluctuate just in step with the 
pulses of the voice waves. This fluctuating direct current 
passes through the primary of an induction coil, producing 
in the secondary an intensified alternating current. This 
passes over the line wires to the receiver where it produces 

460 



WIRELESS TELEPHONY 46 1 

variations in the magnetic field affecting the receiver 
diaphragm, causing the latter to reproduce the voice of 
the person speaking in the transmitter. Now to make 
the comparison clear, two facts must be noted with regard 
to the wire telephone: first, there must be an action 
in the transmitter which causes variations in a current 
through the instrument; second, this fluctuating current 
produces a more intense alternating current which flows 
over the line and affects the receiver diaphragm, produc- 
ing there sound vibrations of greater intensity than those 
used at the transmitter. This added energy comes from 
the current flowing through the transmitter. The case is 
analogous to that of an electric bell. The armature of 
the bell vibrates with greater energy than is required 
to push the button, the extra energy being derived from 
the battery. 

426. The Action of the Wireless Telephone. In the 
wireless telephone we have a continuous stream of electric 
waves of high frequency. (See Fig. 425^4.) This stream 
of electric waves corresponds to the current that flows 
through the transmitter in the wire telephone. These 
waves are of such high frequency that even though we 
had a receiver diaphragm vibrating in step with the 
waves, we could not hear the sound because the 
human ear cannot hear a sound which consists of more 
than about 40,000 vibrations per second. The sound 
waves act upon this stream of waves very much, as in 
the wire telephone, the transmitter acts to modify the 
line current. The impulses caused by the voice are 
much slower than the electric waves first mentioned 
and these slower impulses are reproduced in the receiver. 
Not only are these slower impulses reproduced but they 
are amplified, that is, produced with greater energy than 
the impulses impressed on the stream of waves. Fig. 



462 



PHYSICS 



425^4 represents as nearly as is possible in a diagram the 
continuous stream of electric waves. Fig. 426 5, repre- 




Fig. 425. A, unmodified high frequency waves; B, waves of voice 
frequency; C, high frequency waves modified by waves of voice 
frequency. 

sents the impulses produced by the sound alone, and Fig. 



WIRELESS TELEPHONY 



463 



426 C, shows how these voice impulses are impressed on 
the stream of waves. 

427. The Vacuum Tube or Audion. The device by 
which all of this is accomplished is the vacuum tube. 
(See Fig. 426.) This tube contains three electrodes. 
First, a filament (F, in Fig. 428) which is heated by a 





Fig. 426. Vacuum tube, transmitting Fig. 427. Vacuum tube, 

type. (Western Electric Co.) receiving type. (Western 

Electric Co.) 

current from a battery (Bi, Fig. 428) and because it 
is heated, sends out a stream of electrons. Second, 
the plate which forms the anode of the circuit from 
battery, B 2 . This plate receives the electrons which are 
thrown off by the heated filament, hence a current flows 
through the circuit of B 2 ; the discharge through the tube 
depending on the e.m.f. between the filament and the 



464 



PHYSICS 



plate. Third, a grid is placed between the filament and 
the plate and is connected to the secondary of the induction 
coil, the primary of which is connected to the transmitter. 
When the transmitter diaphragm is vibrating, the e.m.f. 
induced in the secondary of the induction coil causes a 
variation in the potential of the grid. This means a 
variation in the electric field between the filament and 
the plate. (See Fig. 428.) The changing electric field 
causes a variation in the discharge of electrons through 




Fig. 428. Diagram of wireless telephone transmitting set. 



the tube; the variation corresponds to the vibrations 
of the transmitter diaphragm. This produces a surging 
current of the frequency of the sound waves in the primary 
of the transformer (T, Fig. 428). The secondary of this 
transformer is connected to the antennae (A) and the earth 
(E). By means of the transformer, rapid surgings are set 
up in the antennae and these surgings produce a continuous 
stream of electromagnetic waves which goes out in space. 
(Like Fig. 42 6C.) These electromagnetic waves produce os- 
cillations in the antennae of a receiving station. The an- 
tennae transmit the impulses to a tube (Fig. 427) which acts 



WIRELESS TELEPHONY 



465 



as a detector, and makes possible the reproduction of the 
sound by an ordinary telephone receiver. 

The vacuum tube in the transmitting circuit also amplifies 
the impulses, that is, the energy of the waves given out is 
greater than that of the impulses which produce them, 
the additional energy being derived from the battery 




Fig. 429. View of wireless telephone set. 



sending current through the plate and filament. In 
operation, the filament and the plate are connected to a 
battery with a condenser (VC) and an inductance coil 
(I) in the circuit, as shown in Fig. 428. Photograph 
of a complete modern wireless telephone set is shown in 
Fig. 429. 

30 



466 PHYSICS 

Alternating Currents 

428. Alternating currents are of interest to us because 
of their general commercial uSe. To understand the 
reason for the extensive application of alternating currents 
it is necessary to learn the fundamental principles which 
pertain to them. The production of such currents has 
already been explained in Arts. 300-304. It should be 
remembered that the current developed in the armature 
of a dynamo is alternating. A dynamo may deliver a 
direct or an alternating current, depending on the method 
of collecting the current from the armature. If a com- 
mutator is used, the machine delivers direct current, 
if slip rings are employed, an alternating current is 
delivered. 

429. The Magnetic Field of an Alternating Current. 
The magnetic field of a direct current has been considered 
in Arts. 255-256. It has been shown to be arranged in 
circles about the conductor, according to the Right Hand 
Rule. (See Figs. 229 and 230.) These facts will help 
one to understand the following experiment: 

If a number of magnetic compasses be arranged in a circle about a 
straight vertical wire carrying a direct current, the compass needles will 
point out a circle about the wire. (See Fig. 430, A.) If now the cur rent be 
reversed the compass needles will reverse themselves and point in a direc- 
tion just opposite to that taken at first. (See Fig. 430. B) This will be clear 
if you imagine yourself walking around the wire in the direction the com- 
pass needles pointed at first, and then walking around the wire in the 
reverse direction. This illustrates what happens in the field of an alternat- 
ing current. The field reverses each time the current reverses. 

The magnetic field of an alternating current not only 
rapidly reverses itself, but also continually changes in inten- 
sity. At the instant when the current reverses, the force of 
the magnetic field is zero since the current at that instant 
is zero. As the current begins flowing and increases 



WIRELESS TELEPHONY 



467 



to its maximum intensity, the magnetic field appears and 
increases in intensity; and as the current decreases to zero, 
the magnetic field changes in a similar manner. The 
field as it grows in strength extends farther and farther 
from the wire, as it decreases in strength it contracts 
or draws closer to the wire. Thus the magnetic field may 
be said to expand and contract. We may picture the 
lines of force as continually moving. In a typical a.-c. 
circuit, the complete series of changes takes place in a 



*~ 






' 





e 


_ 



A 


B 



Fig. 430. Arrangement of compasses about a wire carrying an alternat- 
ing current. 

small fraction of a second, and is repeated many times 
over in a second. Contrast this with the magnetic field 
of a constant direct current. Here the magnetic field 
has the same direction as long as the current flows and 
does not change in strength. This comparison is im- 
portant because most of the differences between direct 
and alternating currents depend on differences in the 
action of their magnetic fields. 

430. Transformers. The transformer has been de- 
scribed in Arts. 309-3 10. The principle of the transformer 
may be illustrated by the following experiment: 

A coil having several hundred turns of No. 18 d.c.c. copper wire is 
placed over one arm of a "U" shaped iron core (see Fig. 431) and then 



468 



PHYSICS 



connected to a 1 10 volt a.-c. lighting circuit. Another coil (5) having about 
50 turns of No. 22 d.c.c. copper wire is connected to an electric bell or 
buzzer, or a low voltage electric light bulb. When the small coil is held 
over the other arm of the "U" shaped iron core, the bell rings or the 
bulb glows. It is evident that the electromotive force developed in the 
small coil (5) is due to the alternating magnetic field surging back and 
forth through the iron core. In Fig. 431 the core is "open" since the 
magnetic field must pass through the air from one end of the core to the 
other. A typical transformer has a dosed core to provide a closed mag- 
netic circuit. To secure this, take a suitable bar of iron and lay across 
the end of the U" shaped core, and notice any change in the induced 
current produced in the small coil, due to increased movement of mag- 
netism through the closed iron core. 




Fig. 431. Diagram of a transformer. 

This experiment illustrates the construction and action 
of a transformer. In a commercial transformer, the two 
windings are on a closed magnetic circuit. (See Figs. 
304 and 305, p. 346.) To keep the coils insulated, the 
transformer is placed in an iron "housing" and covered 
with oil. These " housings, " or transformer cases are 
generally attached to poles near buildings in which alter- 
nating current is used. 

431. Voltage Relation in a Transformer. In the 
experiment described above, a bell was rung by an induced 
current produced in the secondary coil. The induced 
e.m.f . was less than the voltage of the primary coil partly 
because there was some magnetic leakage, but mainly 



WIRELESS TELEPHONY 469 

because there were fewer turns of wire on the secondary. 
In a commercial transformer the magnetic leakage is 
practically zero. In such a case, the ratio of the number 
of turns on the primary coil to the number on the secondary 
equals the ratio of the e.m.f. induced in the primary to the 
e.m.f. induced in the secondary. Suppose, for example, 
we wish to make a bell ringing transformer to use on a 
no volt lighting circuit, 10 volts being required for the 
bell; the secondary will then need one-eleventh of the 
number of turns of the primary. So that if 550 turns 
are on the primary, then 50 turns will be needed for the 
secondary. This will be a ""step-down" transformer. 
On the other hand, suppose we wish to "step-up" the 
voltage as is done in a certain power station where the 
voltage of the generators is 6000 volts, the voltage being 
stepped up to 44,000 by means of large transformers. 
This means that the secondary coils have approximately 
7^3 times as many turns as the primary. 

432. Power Loss in a Transformer. When the voltage 
is "stepped up" in a transformer, do we gain power? 
To answer this question we must remember that electric 
power does not depend on voltage alone but on the product 
of e.m.f. and current intensity. (See Art. 291.) By 
tests with a.-c. voltmeters and ammeters, we find that 
when the secondary e.m.f. is greater than the primary 
e.m.f., the secondary current intensity is less than 
that in the primary. It is also found that the power 
developed is less than the power received by the trans- 
former, i.e., the "output" is less than the "input" as 
we would expect from the law of machines. The power 
loss is mainly due to the work required to reverse the 
magnetism, that is, to continually reverse the position 
of the iron molecules. (See Art. 205.) The energy lost 
in this manner is known as " core loss " since it occurs in the 



47 



PHYSICS 



iron core. The lost energy appears as heat. So much 
heat is developed in large transformers that special means 
of cooling are provided. In order to make the heat 
developed as small as possible, the cores are "laminated" 
(see Fig. 305, p. 346), that is, built up of thin sheets of 
iron, because if the iron cores, were solid, the changing 
magnetic fields would induce electric currents in the 
iron cores, which would produce an excessive amount of 
heat with a correspondingly large power loss. 

433. Choke Coils and Inductance. If we refer to Fig. 
432 we see that the primary winding of the bell ringing 




Fig. 432. Diagram of "bell-ringing" transformer. 

transformer is connected across the line. This winding 
forms a closed circuit whether the bell is ringing or not. 
The resistance of this winding is small. Let us assume 
it to be one ohm. With a one ohm resistance connected 
across a no volt line we might expect a current of no 
amperes. This is certainly what we should get if we were 
to connect a one ohm resistance across a line having no 
volts direct. The primary would form a short circuit 
if the current were direct. But the fact is that practically 
no current flows through the primary winding when the 
bell is not ringing. Herein lies one of the important dif- 
ferences between alternating and direct currents. With 
an alternating current the primary winding of our trans- 



WIRELESS TELEPHONY 



471 



former acts as a choke coil and "chokes" down the current 
almost to zero. Let us see how this is done. 

Let Fig. 433 represent a choke coil. Since alternating 
current is used, the magnetic field is continually changing. 
Each turn of wire has its own magnetic field. The lines 
of force of turn number 1 expand and contract and as 
they do so they move across turns 2, 3 and so on. In 
like manner the lines of force from each turn of wire move 
across the other turns. In other words the coil is cutting 
its own lines of force. Now whenever an electric con- 
ductor cuts magnetic lines of force an electromotive 




Fig. 433. A circuit containing a choke coil. 

force is induced in the conductor. There is then an e.m.f. 
induced in the coil by its own magnetic field. This in- 
duced e.m.f. on the whole opposes the applied e.m.f.; 
in the primary of our bell ringing transformer the in- 
duced e.m.f. opposes the e.m.f. of the line to such an 
extent as to reduce the current almost to zero. In- 
ductance is the action of an alternating current in inducing 
an opposing e.m.f. in the coil in which the current is flow- 
ing. Since this opposing e.m.f. is induced in the coil by 
its own magnetic field this action is also called self-induction. 
in a transformer the action of the field of the primary upon 
the secondary is mutual induction; while the action of the 
field of the primary in choking the current in the primary 
itself is self-induction or inductance. A coil having a 
single winding and used to introduce inductance in a 



472 



PHYSICS 



circuit is called a choke coil. A choke coil inserted in a 
lamp circuit in series with the lamps dims the lamps 
because it reduces the intensity of the current. 

Self-induction causes the current to lag, that is, the cur- 
rent does not quite reach its maximum at the instant the 
voltage reaches its maximum. Fig. 434 shows graphically 
an e.m.f. and a lagging current. In this figure the maxi- 
mum current is shown following the maximum voltage at 
an interval of 30 degrees. In other words the armature in 



Graph of Erlfand Current Showing Lag 




Fig. 434. Diagram showing graphically an alternating current with a 
"lag" of 30 behind its electromotive force. 



a two-pole field must turn 30 degrees from the position of 
maximum voltage before the current in the coil, where the 
self-induction occurs, reaches its maximum. 

434. Reactance and Impedance. A choke coil has re- 
sistance as well as inductance. Its resistance can be found 
by the voltmeter-ammeter method, using a direct current. 
(See Art. 278.) Let us take for example the primary wind- 
ing of a bell ringing transformer. Using a direct current 
and testing the coil with a voltmeter and ammeter we find 
its resistance to be, let us say, one ohm. If we connect the 
same coil across a no volt a.-c. line we find the current 



WIRELESS TELEPHONY 



473 



to be very small, say 0.05 ampere. The coil now has 
resistance and reactance. Reactance is the effect of 
self-induction in hindering the flow of current. It is 
measured in ohms. The combined effect of resistance 
and reactance is called impedance. In the example 

no (volts) 



above, the coil has 



= 2200 ohms of im- 



0.05 (ampere) 
pedance. In applying Ohm's law to an alternating current 
circuit, impedance must be substituted for resistance. 
Ohm's law as applied to an a-c. circuit should be stated: 





& 




K 




<^% 







^^ 


9 













p> 







[Rj RESISTANCE. 
Fig. 435. The relation between resistance, reactance and impedance. 



"Current intensity equals e.m.f. divided by impedance", 
or I = E/Z. (Z = impedance.) 

Impedance, however, does not equal the sum of resis- 
tance and reactance. The relation between these three 
quantities is similar to that between the three sides 
of a right triangle, in which the impedance represents 
the hypotenuse, and the resistance and reactance the 
other two sides. See Fig. 435 which indicates that 
Resistance 2 + Reactance 2 = Impedance 2 , or (R 2 + X 2 = 
Z 2 ). (X = reactance.) To illustrate this relation; sup- 
pose the primary of a transformer has 10 ohms impedance 
and 8 ohms resistance, then the reactance equals io 2 8 2 
= 6 2 , or the reactance is 6 ohms. 



474 



PHYSICS 



Exercises 

i. Find the reactance of a choke coil having a resistance of 10 
ohms, when its impedance is 50 ohms. How great a current flows 
through this coil if the terminal voltage is no volts? 

2. When the bell is ringing, the primary of a bell ringing trans- 
former has an appreciable current. Suppose this current is 0.2 
ampere. What is the impedance if the voltage of the line is 115 
volts? What is the reactance if the resistance is 1 ohm? 

3. The primary of a large transformer has a terminal voltage 
of 6000 volts and a current of 600 amperes. What is the imped- 
ance? If the resistance is 6 ohms, what is the reactance? 

435. The electric condenser (see Art. 231) is a 
very useful device in a.-c. circuits; e.g., in telephone sets 




Transm/iten 



Fig. 436. A telephone set showing a condenser used in the circuit of the 

"ringer." 

used in cities, a condenser is used in the ringing circuit, 
as shown in Fig. 436. Alternating current is required to 
ring such a bell and a condenser permits an a.-c. current 
to act through it, although it entirely prevents the flow of a 
direct current. This peculiar action will now be explained. 
436. The action of a condenser in an alternating cur- 
rent circuit may be illustrated by the following experiment. 
Connect twelve, 1 m.f . (microfarad) condensers, in parallel, 
and then attach them to a no volt a.-c. line so that an 



WIRELESS TELEPHONY 475 

incandescent lamp is in circuit as shown in Fig. 437. 
The lamp will be found to glow brightly, although there 
is no electrical connection between the two sets of conden- 
ser plates. If the same arrangement is connected to a 
no volt direct current circuit, the lamp does not 
glow because it is really an open circuit. The lamp glows 
on an a.-c. circuit because, although no electricity flows 
through the condenser, it does flow into and out of the 
condenser, surging back and forth through the lamp with 
sufficient intensity to cause it to glow brightly. When 
the a.-c. current moves one way in the circuit, one set 



llO-VA.C. 



Fig. 437. Twelve condensers in circuit with an incandescent lamp. 

of plates of the condensers becomes charged positively, 
the other, negatively. When the a.-c. current reverses, 
the charges on the condenser plates reverse. In the 
ordinary lighting circuit 120 reversals take place each 
second, so that electricity rapidly flows into and out of the 
condensers. On removing one condenser after another 
from the circuit, the lamp is found to glow less and less, 
till when but one condenser is left, no glowing is observed, 
since one small condenser does not have sufficient capacity. 
The unit of capacity is the Farad. Capacity is defined 
as the quantity of electricity per second that flows into a 
condenser when the voltage at the terminals changes at 
the rate of one volt per second. If a change of one volt 
per second causes one coulomb to flow per second, that 
is, a current of one ampere, the capacity is one. farad. 
The condensers used in the above experiment have a 
capacity of one microfarad, or one millionth of a farad. 



476 physics 

A condenser, on account of its capacity, causes an a.-c. 
current to lead the voltage, that is the current reaches 
its maximum value before the voltage does. In this 
respect a condenser has an effect opposite to that of the 
s*elf-induction of a choke coil (the latter causing the 
current to "lag")- (See Fig. 435.) 

437. Transmission of Electric Power. A field of 
peculiar usefulness for a.-c. currents is in the economical 
transmission of electric power. This fact is due to the 
following reasons: (a) The loss of electrical power in a 
transmission line is due to the production of heat; the 
heat produced being proportional to PR, or to the square 
of the current intensity. Any lessening of the current 
flow required to transmit a given power wilj therefore 
increase the efficiency of transmission, (b) In order 
to employ a small current in transmitting a large amount 
of power, we must use a very high e.m.f. Such high 
electromotive forces, say from 60,000 to 100,000 volts, 
can be obtained only by the use of a.-c. transformers, 
since it is not practicable to build a direct current gener- 
ator capable of producing 60,000 volts. In large power 
transmission systems, a.-c. generators are used to produce 
powerful alternating currents. The e.m.f. is then stepped 
up to a suitable voltage (2300100,000) by transformers 
and sent over transmission lines to the various places 
where the power is to be used; at these places suitable 
transformers "step-down" the e.m.f. to a convenient or 
safe voltage for use. (See Fig. 442 of a transmission 
line and Fig. 438 of a large power transmission system, 
and Fig. 439 of an a.-c. generator and power plant.) 

438. Power Factor. The power factor is a matter of 
interest and importance in the use of a.-c. machines. 
It meaning and use may be learned from the following 
explanation: In a direct current circuit, watts equals 



WIRELESS TELEPHONY 



477 




478 



PHYSICS 



volts times amperes. In an alternating current circuit, 
this equation is true only when the current is "in step" 
with the voltage, that is, only when there is no in- 
ductance or capacity in the circuit. If current and 
voltage are out of step, i.e., if there' is lag or lead (see 
Fig. 434), the product of volts and amperes gives only 
the apparent power, the ratio between true and apparent 




Fig. 439. Power house showing alternators, direct connected to 
horizontal hydraulic turbines. Note the direct current "exciter" on 
end of shaft of alternator. (Courtesy of General Electric Co.) 

power depending on the amount of lag or lead. This ratio 
is called the power factor. In an a.-c. circuit, then, the 
power equation is: watts = volts X amperes X power 
factor, or power factor = true power/ apparent power. 
The products of volts and amperes is the apparent power 
and is called volt-amperes in distinction from the true 
power or watts. Therefore the following is true: power 
factor = true watts/ volt-amperes. 



WIRELESS TELEPHONY 



479 



439. Single-phase Currents. There are several kinds 
of a.-c. currents. One of the most common is the single- 
phase. It is simply the common a.-c. current used for 
light and power in the average home, and uses a two-wire 
circuit around which the current is rapidly alternating. 
Fig. 440 illustrates the changes of e.m.f. in an a.-c. single- 
phase current. It may be produced by a single coil 
rotating in a magnetic field. The curve of Fig. 440 rep- 
resents one cycle, that is, one complete series of changes in 




Fig. 440. Graph showing the e.m.f. changes of a single-phase current 
for one "cycle." 

the electromotive forces. At the end of the cycle the arma- 
ture is in the same condition as at the beginning so far as 
the magnetic field is concerned. It then begins a new 
cycle. The ordinary commercial alternating current has a 
frequency of 60, that is 60 cycles per second. One rota- 
tion produces as many cycles as there are pairs of poles. 
For example, if there are 48 poles in the generator field, 
one rotation produces 24 cycles. 

440. Three-phase Currents. Now suppose we have 
three coils as in Fig. 441, the coils being evenly spaced, 
or 120 degrees apart, at A, B, and C. If the coils are 
rotated in a magnetic field, each will produce an electro- 



480 



PHYSICS 



motive force. The result produced by three such coils 
is called a three-phase current. Ordinarily six wires, or 
three circuits, would be required to carry the current pro- 
duced by three separate coils; for when coil "C" is in the 
90 degree position, where its e.m.f. is a maximum, coil "3" 
is 120 degrees past its maximum, and coil "A" is 240 de- 
grees past its maximum. The graph (Fig. 441) shows the 
maximum points of the three e.m.f's. separated by inter- 
vals ,of 120 degrees. In practice, however, it is found 
possible to use three wires instead of six, as explained in 
Art. 441. 



N 



. fir for- co// A. 

.nr force// c 




Fig. 441. Graph showing the e.m.f. changes of a three-phase current 
for one "cycle." 

441. Three-wire Transmission. The currents produced 
in the three coils just described undergo precisely the 
same changes as those represented in the graph (Fig. 441) 
for the three electromotive forces. Careful examination 
of the graph will show that at any point the sum of the 
plus e.m.f's. equals the sum of the minus e.m.f's. In 
other words the algebraic sum of the three e.m.f's. is 
zero. Therefore if we properly connect a transmission 
line of three wires to the generator, the sum of the currents 



WIRELESS TELEPHONY 



481 



leaving the generator will equal the sum of the currents 
returning to it. Since the algebraic sum of the currents 
produced by the three coil combination described in Art. 
440 is always zero, it is possible to use three wires on 
three-phase transmission lines. Fig. 442 shows a "tower" 
carrying three, three-wire transmission lines. Long 




Fig. 442. A "tower" supporting three, three-phase circuits of a high 
tension transmission line. 

distance, high tension transmission lines are generally 
three-wire lines carrying three-phase a.-c. currents. 

442. Alternators. A dynamo which delivers alternating 
current is known as an alternator. Commercial alternators 
have many pairs of poles in the field and as a rule the 
field rotates while the armature is stationary. The field 
must be supplied with direct current for the polarity of 
each coil in the field must remain unchanged. Usually 
31 



482 



PHYSICS 



a separate "exciter" is used, which is a small direct 
current generator. The current from this exciter is fed 
into the rotating field by means of slip rings. Fig. 439 
shows a d.-c. (direct current) exciter on the end of the 
armature shaft of the large alternator. 

443. The A.-C. Series Motors. The only type of 
motor that will run on either alternating or direct current 
is the series motor. The "universal" motor used in 




Fig. 443. Diagram of a "Series Motor." 

household appliances such as electric fans, vacuum 
cleaners, etc., is a series motor. The reason a series motor 
will run on either direct or alternating current is because 
the direction of rotation of the armature of a motor 
depends on (a) the direction of the current in the armature, 
and (b) the polarity of the field. Reversing either of 
these alone, reverses the direction of rotation of the arma- 
ture, while reversing both at the same instant leaves 
the direction of rotation unchanged. Fig. 443 is a 
diagram of a series motor since the field coils and armature 



WIRELESS TELEPHONY 



483 



are connected in series. On an a.-c. line, both field and 
armature current must therefore reverse at the same 
instant. In a shunt motor (similar to Fig. 286) we have 
a divided circuit, and the greater self-induction of the 
field coils causes an a.-c. current through these coils to lag 
behind that flowing in the armature so that the two 
currents do not reverse at the same instant. 

444. The Induction Motor. Another common type of 
a.-c. motor is the induction motor. Its advantage lies in 
its simplicity. It has neither commutator nor brushes, 




THREE PHASE FROM SINGLE PHASE 

Fig. 444. Diagram of a gramme ring. It is shown connected to a 
single-phase current so as to produce a rotating magnetic field, similar 
to that obtained with a three-phase current. (Ahrens, Harley and Burns.) 



the armature having no connection with an external cir- 
cuit. If the wires of a three-phase line be connected 
to a coil wound in the form of a gramme ring, the connect- 
ions being 1 20 degrees apart as in Fig. 444, the magnetic 
field within this coil will change in the same manner as if a 
magnet were spinning upon a pivot at the center of the 
coil. Suppose the N pole at one instant is at A, in one- 
third of a cycle it moves to B, in another third to C, 
and in one cycle it makes a complete revolution. Thus 
we have a rotating magnetic field. If a cup of some non- 
magnetic metal such as aluminium or copper be placed 
on a pivot in the center of this coil, the cup is cut by the 



4 8 4 



PHYSICS 



moving lines of force and currents are induced in it. 
Because of these currents, the cup has a magnetic field 
of its own, and the action of the two magnetic fields is 
such as to pull the cup around and cause it to rotate in the 
same direction as that in which the field of the coil rotates. 
The coil represents the stationary part, the stator (Fig. 445) 
and the cup the rotating part, the rotor, of an induction 




Fig. 445. The "stator" of an induction motor. 



motor. While the cup rotates in the same direction, it does 
not rotate so rapidly as the magnetic field. If it should it 
is plain that it would not cut the lines of force. The dif- 
ference between the rate of rotation of the rotor and that 
of the magnetic field is called the "slip." The rotating 
part in small induction motors is frequently made in a 
single casting. In large motors, it is built up of heavy 
copper bars. Thus, from its appearance the common form 



WIRELESS TELEPHONY 



485 



of rotor is known as the "squirrel cage" rotor. (See 
Fig. 446.) 




Fig. 446. The "rotor" of an induction motor. 

445. A synchronous motor is one that keeps step with 
the alterations of an alternating current. The line current 
is fed into the armature by means of two slip rings and 




Fig. 447. Diagram illustrating the principle of the synchronous 
motor. The armature coil passes the position shown in the figure at the 
instant the current in the line reverses. Thus the armature keeps 
with the line current, making one revolution with each "cycle." 

brushes. The principle of the synchronous motor is 
illustrated in Fig. 447. This shows a motor having a 
two-pole field. The armature current must be reversed 



486 PHYSICS 

twice in each revolution. The reversal must take place 
when the armature winding is perpendicular to the lines 
of force of the field. In a direct current motor this 
reversal is brought about by the commutator. In a 
synchronous motor the armature reaches the 90 degree 
position at the exact instant at which the current reverses 
in the line. Thus in the case of a two-pole motor the 
armature must make exactly one revolution for each 
cycle; it is, therefore, a constant speed motor. Such 
motors are frequently employed in converter stations 
where alternating current is converted into direct current 
by what are called rotary converters. 

In practice the synchronous motor has a number of pairs 
of field poles. It is essentially an alternating current 
generator running as a motor. One of the principal uses 
of the synchronous, motor is that of a converter, receiving 
alternating current and delivering direct current. Syn- 
chronous motors are also used in transmission lines to aid 
in maintaining constant voltage. 

Important Topics 

The wireless telephone, essential parts, action, arrangement. 
Alternating currents, alternating fields. 

Transformers, voltage relation of coils, power and core losses. 
Self-induction, inductance, and coke coils, uses, applications. 
Impedance, reactance, and resistance; relation and effects. 
Condensers, uses and applications with a-c. circuits. 
Alternating current power transmission; uses, advantages. 
Power factor, lag, lead, volt-amperes, true watts. 
Single- and three-phase currents; uses and nature of each. 
Three-wire transmission systems, alternators, construction, and 
action. 

A-c. motors, series, induction, synchronous. 



INDEX 



Aberration, spherical, 408 
Absolute scale of temperature, 

164 
Absorptions of gases by solids 

and liquids, 29 
Accelerated motion, 86 
Acceleration, 87 
Adhesion, 21 
Aeroplane, 97 
Air, aspirator, 67 

brake, 74 

cushion, 46 

height (of atmosphere), 64 

pressure, 56 

pump, 66 

weight, 56 
Alternators, 481 
Alternating current, 337, 466 
Amalgamation, 273 
Ammeter, 291 . 
Ampere, 291 

Archimedes' principle, 48 
Arc light, 32 1 
Armature, 335 
Artesian wells, 44 
Audion, 463 
Aurora borealis, 453 

Balloon, 72 
Barometer, 59 
Beats, 376 
Boiling, laws, 208 

point, 207 
Boyle's Law, 63 
Breezes, land and sea, 181 
British thermal unit, 162 
Brownian movements, 16 

Calorie, defined, 162 
Camera, 426 
Candlepower, 394 
Capillary action, 25 
Cartesian diver, 71 
Cathode rays, 453 
Centrifugal force, 91 
Charles' Law, 165 



Chladni's figures, 381 
Choke coils, 470 

Coefficient of expansion, defini- 
tions, 170 

gases, 167 

liquids, 168 

solids, 169 
Coherer, 449 
Cohesion, 21, 33 
Color, 435 

bodies, 435 

complementary, 436 

primary, 440 

prismatic, 433 

theory of color vision, 440 

three-color printing, 440 
Commutator, 335, 336 
Compass, 230, 240 
Concave lens, 418 
Condenser, 260, 474 
Conductors, 246 
Conservation of energy, 127 
Continental code, 459 

compared with the Morse, 
.452 
Convection, 179 

currents in nature, 181 

draft of a chimney, 180 
Convex lens, 416 
Cooling, artificial, 210 
Corpuscular theory, 442 
Coulomb, 290 

meter, 291 
Couple, 101 
Critical angle, 414 
Crookes' tube, 456 
Crystallization, 28 

melting point of some crys- 
talline substances, 203 

Daniel cell, 276 
Declination, 240 
Density, 38, 52 

methods for finding, 53 
Dew, 192 
Dew point, 193 



487 



488 



INDEX 



Diffusion of' gases, 1 3 
Dipping needle, 240 
Direct Current, 337 
Dispersion, 433 
Distillation, 208 
Draft of a chimney, 180 
Dry cell, 275 
Dynamo, 330, 333 
Dyne, 93 

Eye, the, 423 

action of, in vision, 423 

defects of, 425 
Ear, the, 386 

trumpet, 361 
Earth's magnetism, 238 
Echoes, 362 
Eclipses, 391 
Efficiency, 142 

engines (tests), 219 

machines, 142 
Elasticity, 31 
Electric bell, 269, 287 

charge, distribution of, upon 
a conductor, 253 

circuit, 269 

currents, 267 

single phase, 479 

three phase, 479 

effects, 277 

induced, 326 

' discharge m rarefied air, 452 

motor, 339 

screen, 256 
Electrical capacity, 259 

fields, 247 
Electrification, 243 
Electrolysis, 308 

laws, 311 

practical uses, 311 
Electromagnet, 281 
Electromagnetic theory of light, 

45.6 
Electromotive force, 267 

unit of, 295 
Electron theory, 252 
Electrophorus, 263 
Electroplating, 307 
Electroscope, 244 
Electrostatic induction, 248 
Energy, 120 

conservation, 127 

falling water, 152 

forms, 125 

human body, 126 



Energy, kinetic, 121 

potential, 120 

transference and transforma- 
tion, 124 
Engines, 213 
Engines, gas, 222 

steam, 213 
turbine, 225 
Equilibrant, 81 
Equilibrium, 106 

neutral, 107 

stable, 106 

stability, 108 

unstable, 107 
Erg, 119 
Ether, 177 
Evaporation, 18 

cooling effect, 19, 197 

rate, 198 
Expansion, coefficient, 168 

gases, 167 

liquids, 168 

peculiarity, in water, 168 

solids, 169 

water, on turning to steam, 
206 



Falling bodies, 109 

experimental study, ill 

laws, 113 
Floating bodies, 48 
Flouroscope, 455 
Foot candle, 396 
Force, 79 

dyne, 93 

effectiveness, 134 

graphic representation, 80 

liquid, against any surface, 
38.. 

measuring, 79 

moment, 99 

parallel, 100 

resolution, 96 

units, 83 
Forces, parallel, 100 
Franklin's theory of electricity^ 

252 
Fraunhofer lines, 439 
Freezing, evaporation, 197, 199 

mixtures, 210 
Friction, 147 

coefficient, 149 

fluid, 150 

kinds, 147 



INDEX 



489 



Friction, laws, 150 
reducing, 148 
uses, 149 

Galvanometers, 289 
Galvanoscope, 269 
Gas engine, 222 

efficiency of, 224 
Gas meter, 75 
Geissler tubes, 453 
Gravitation, 103 

law, 104 
Gravity, 88, 104 

acceleration due to, 1 1 1 

cell, 277 

center of, 105 

Hail, 193 

Hearing, 386 

Heat, capacity for water, 201 

conduction, 173 

constants for transmission, 
220 

convection, 179 

effects, 161 

engines, 213, 222 

equivalent of fuels, 219 

fusion, 201 

measurement, 200 

methods of transmitting, 173 

produced by electric current, 

.318 

radiation, 176 

sources, 159 

units, 162 

vaporization, 205 

work, 212 
Heating of buildings, 182 

direct and indirect radiation, 
186 

hot air, 183 
water,- 186 

plenum system, 187 

steam, 186 

vacuum steam, 187 

vapor steam, 187 
Hertzian waves, 262, 449 
Hooke's law, 33 
Horse power, 123' 

electric equivalent of, 123 
Humidity, 194 
Hydraulic press', 42 

elevator, 44 

ram, 72 
Hygrometers, 194 



Hygrometry, 191 

conditions for saturation, 
192 

dew point, 193 

fog, 193 

formation, of dew, 192 

humidity, 194 

hygrometers, 194 

importance, 191 
Hypothesis, 3 

Images, concave mirrors, 405 

construction, 405 

definition, 392 

plain mirror, 401 

small apertures, 391 
Impedance, 472 
Incandescent lamp, 320 
Inclined plane, 143 
Inductance, 471 
Induction coil, 343 
Inertia, 87 
Insulators, 246 
Intensity of sound, 363 
Interference, light, 442 

sound, 374 

Joule, 120, 319 

Laws, boiling, 208 

Boyle's 63 

Charles, 165 

electric action, 243 

falling bodies, 113 

floating bodies, 48 

gravitation, 104 

Hooke's, 33 

induced currents, 326 

intensity of light, 394 

Lenz's, 328 

liquid pressure, 37 

machines, 131 

magnetic action, 229 

motion, 87 

Ohm's, 298 

pendulum, 116 

reflection, 399 

refraction of light, 411 

vibration of strings, 378 
Lenses, achromatic, 434 

effect on light, 417 

equation, 421 

formation of images, 418 ' 

forms, 416 
Le Clanche cell, 275 



49 



INDEX 



Lever, 132 
Leyden jar, 261 

oscillatory nature of the 
discharge, 448 
Light, compared with sound, 388, 

444 

electromagnetic theory, 456 

intensity, 394 

interference, 442 

polarization, 445 

rectilinear propagation, 389 

reflection, 396 

total reflection, 413 
Lightning, 254 
Lines, of force, 233 

agonic, 240 

isogonic, 240 
Liquids, pressure, 36 
Local action, 273 
Luminous and illuminated bodies, 
388 

Machines, 129 

advantages, 129 
cannot create energy, 130 
efficiency, 142 
law, 131 

mechanical advantage, 134 
the six simple, 132 
uses, 129 
Magnetic action, 229 
fields, 233, 466 
induction, 231, 236 
permeability, 237 
poles, 229 
properties, 230 
retentivity, 231 
substances, 230 
effect of electric current, 279 
Magnetism, 228 
Magnetism, theory, 232 
Major and minor triads, 369 
Magneto, 328 
Magnetoscope, 230 
Magnets, 228 
poles, 229 
Major scale, 366 
Manometric flames, 382 
Matter, 4 

effect of heat, 5 
molecular theory, 5 
properties, 34 
states of, 4 
states of, defined, 5 
Mechanical advantage, 134 



Megaphone, 365 
Melting points, 203 
Mercury arc rectifier, 347 
Metric system, 8 
Microscope, 427 
Mirage, 414 
Mirrors, 400 

concave, 405 

convex, 407 

parabolic, 409 

plane, 401 
Molecular motion in liquids, 18 

in gases, 13 

in liquids and solids, 27 

in solids, 31 
Molecules, motion, 16 

size, 13 
Moment of force, 99, 133 
Momentum, 87 

law of, 92 
Motion, 85 

accelerated, 86 

curvilinear, 8 

direction, 86 

first law, 87 

modes, 85 

second law, 92 

third law, 93 

uniformity, 86 
Motor (electric), 339 

A. C. series, 482 

induction, 483 

synchronous, 485 
Muffler, 224 
Musical instruments, 377 

interval, 368 

nomenclatures, table, 369 
Musical sounds, characteristics, 
364 

Newton's Laws of motion, 87 
Nodes, in pipes, 384 

in strings, 379 
Noise and music, 363 

Ohm, 294 
Ohm's Law, 298 
Opera glass, 428 
Optical illusions, 390, 404 
instruments, 423 

camera, 426 

eye, 423 

microscope, 427 

opera glass, 428 

prism field glass, 429 



INDEX 



491 



Optical illusions, instruments, 
projecting lantern, 427 
telescope, 428 
Organ pipes, closed, 384 

nodes, 384 

open, 384 
Oscillatory discharge, 448 
Osmosis, 19 
Outline Review, 

current electricity, 325 

force and motion, 118 

heat, 227 

induced currents, 353 

light, 446 

magnetism and static elec- 
tricity, 266 

sound, 387 

work and energy, 158 
Overtones, 379 

Pascal's principle, 41 
Pendulum, compound, 115 

laws, 116 

simple, 115 

uses, 116 
Pepper's ghost, 404 
Permeability, 237 
Phonograph, 383 
Physics, definition, 4 
Photometer, 394 
Photometry, 393 
Pitch, 365 
Polarization, of light, 445 

of voltaic cells, 273 
Portraits, 

Bell, 431 

Edison, 285 

Faraday, 331 

Galileo, 89 

Gilbet, 217 

Helmholtz, 397 

Huygens, 397 

Joule, 217 

Kelvin, 331 

Marconi, 431 

Morse, 285 

Newton, 89 
Potential, 257 
Power, 123 

electric, 316 

power factor, 476 

transmission of electric, 476 

water, 152 
Pressure, air, 56 

atmospheric, 58 



Pressure, definition, 37 

effect on liquids and gases, 
62 

law of liquid, 37 
Prism field glass, 429 
Projecting lantern, 427 
Proof-plane, 244 
Pulley, 139 
Pumps, air, 66 

condensing, 67 

water (lift, 68, force, 69) 

Quality of musical tones, 380 

Radiation, 176 

sun's 178 
Radio-activity, 457 
Radiometer, 177 
Radium, 457 
Rainbow, 436 
Reactance, 472 
Reflection, light, 396 

multiple, 404 

sound, 360 

total of light, 413 
Refraction, 410 

cause, 412 

index, 412 

light, 410 

in plates, prisms, and lenses, 

413 
Resolution of forces, 96 
Resistance, cells in series, and 
parallel, 302 
conductors, 293 

in series and parallel, 299, 
300 
unit, 294 

volt-ammeter method for 
finding, 304 
Resonance, 371 
Resonator, 373 
Resultant, 81 
Retentivity, 231 
Right hand rule, 279 
Rotary convertor, 486 

Science, definition, 2 
Screw, 144 
Shadows, 390 
Single phase currents, 479 
Siphon, 70 
Siren, 366 

Solidification, change of volume 
during, 203 



492 



INDEX 



Solutions, 27 

Sound, compared with light, 388 

interference, 374 

media, 355 

nature, 356 
, reflection, 360 

rule for finding velocity, 367 

source, 354 

speed, 355 

transmission in air, 359 
Specific heat, 200 

method of determining, 201 
Spectroscope, 438 
Spectrum, 433 
Spherical aberration, 408 
Spinthariscope, 458 
Stability, 108 
Standpipe, 46 

Static and current electricity 
compared, 287 

electrical machines, 262 
Steam engine, 213 

turbine, 225 
Storage battery, 312 
Stress and strain, 94 
Sublimation, 199 
Surface tension, 22 
Sympathetic vibration, 372 

Telegraph, 283 

wireless, 450 
Telephone, 49 

receiver, 349 

transmitter, 350 

wireless, 460 
Telescope, 428 
Temperature, 162 

absolute scale, 164 
Tempered scale, 370 
Theory, 3 
Thermometer, air, 167 

centrigrade, Fahrenheit, 163 

gas, 167 
Thermos bottle, 176 
Thermostat, 188 
Three-color printing, 440 
Three phase currents, 479 



Three wire transmission, 480 
Torricelli's experiment, 57 
Trade winds, 182 
Transformer, 345, 467 

uses, 347 
Turbine, steam, 225 

water, 154 

Vacuum cleaner, 76 

pan, 210 
Velocity, 86 
Vibration strings, 378 

sympathetic, 372 
Visual angle, 424 
Viscosity, 20 
Volt, 295 
Voltaic cell, 270 

advantages, 274 

amalgamation, 273 

local action, 273 

polorization, 273 

simple, 270 
Voltmeter, 295 

Water wheels, 152 

overshot, 152 

turbine, 154 

undershot, 153 
Watt, 123, 317 
Wave theory, of light, 442 
Waves, beats, 376 

interference, 374 

longitudinal, 358 

sound, 358 

transverse, 358 

visible, 357 
Wedge, 144 
Weight, 104 
Wheatstone bridge, 304 
Wheel and axle, 136 
Wind instruments, 383 
Wireless telegraphy, 450 

telephony, 460 
Work, 119 

units, 119 

"X" rays, 454 



PLEASE DO NOT REMOVE 
CARDS OR SLIPS FROM THIS POCKET 

UNIVERSITY OF TORONTO LIBRARY 



QC Tower, Willis Eugene 

23 Physics 

T7 



P&iSci.